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Volumn 1, Issue PART B, 2006, Pages 265-326

Chapter 3 Stochastic-Like behaviour in nonuniformly expanding maps

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EID: 33745368100     PISSN: 1874575X     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S1874-575X(06)80028-7     Document Type: Chapter
Times cited : (26)

References (173)
  • 1
    • 67649389588 scopus 로고    scopus 로고
    • Smooth ergodic theory and nonuniformly hyperbolic dynamics
    • Hasselblatt B., and Katok A. (Eds), Elsevier, Amsterdam
    • Barreira L., and Pesin Ya. Smooth ergodic theory and nonuniformly hyperbolic dynamics. In: Hasselblatt B., and Katok A. (Eds). Handbook of Dynamical Systems Vol. 1B (2006), Elsevier, Amsterdam 57-263
    • (2006) Handbook of Dynamical Systems , vol.1 B , pp. 57-263
    • Barreira, L.1    Pesin, Ya.2
  • 2
    • 1042287164 scopus 로고    scopus 로고
    • Invariant measures for hyperbolic dynamical systems
    • Hasselblatt B., and Katok A. (Eds), Elsevier, Amsterdam
    • Chernov N. Invariant measures for hyperbolic dynamical systems. In: Hasselblatt B., and Katok A. (Eds). Handbook of Dynamical Systems Vol. 1A (2002), Elsevier, Amsterdam 321-407
    • (2002) Handbook of Dynamical Systems , vol.1 A , pp. 321-407
    • Chernov, N.1
  • 3
    • 33751347915 scopus 로고    scopus 로고
    • Hyperbolic dynamical systems
    • Hasselblatt B., and Katok A. (Eds), Elsevier, Amsterdam
    • Hasselblatt B. Hyperbolic dynamical systems. In: Hasselblatt B., and Katok A. (Eds). Handbook of Dynamical Systems Vol. 1A (2002), Elsevier, Amsterdam 239-319
    • (2002) Handbook of Dynamical Systems , vol.1 A , pp. 239-319
    • Hasselblatt, B.1
  • 4
    • 67649363660 scopus 로고    scopus 로고
    • Principal structures
    • Hasselblatt B., and Katok A. (Eds), Elsevier, Amsterdam
    • Hasselblatt B., and Katok A. Principal structures. In: Hasselblatt B., and Katok A. (Eds). Handbook of Dynamical Systems Vol. 1 A (2002), Elsevier, Amsterdam 1-203
    • (2002) Handbook of Dynamical Systems , vol.1 A , pp. 1-203
    • Hasselblatt, B.1    Katok, A.2
  • 5
    • 33748479948 scopus 로고    scopus 로고
    • Partially hyperbolic dynamical systems
    • Hasselblatt B., and Katok A. (Eds), Elsevier, Amsterdam
    • Hasselblatt B., and Pesin Ya. Partially hyperbolic dynamical systems. In: Hasselblatt B., and Katok A. (Eds). Handbook of Dynamical Systems Vol. 1B (2006), Elsevier, Amsterdam 1-55
    • (2006) Handbook of Dynamical Systems , vol.1 B , pp. 1-55
    • Hasselblatt, B.1    Pesin, Ya.2
  • 6
    • 67649361716 scopus 로고    scopus 로고
    • One-dimensional maps
    • Hasselblatt B., and Katok A. (Eds), Elsevier, Amsterdam
    • Jakobson M., and Świtek G. One-dimensional maps. In: Hasselblatt B., and Katok A. (Eds). Handbook of Dynamical Systems Vol. 1 A (2002), Elsevier, Amsterdam 599-666
    • (2002) Handbook of Dynamical Systems , vol.1 A , pp. 599-666
    • Jakobson, M.1    Świtek, G.2
  • 7
    • 0042080490 scopus 로고    scopus 로고
    • Hyperbolic dynamics and Riemannian geometry
    • Hasselblatt B., and Katok A. (Eds), Elsevier, Amsterdam
    • Knieper G. Hyperbolic dynamics and Riemannian geometry. In: Hasselblatt B., and Katok A. (Eds). Handbook of Dynamical Systems Vol. 1 A (2002), Elsevier, Amsterdam 453-545
    • (2002) Handbook of Dynamical Systems , vol.1 A , pp. 453-545
    • Knieper, G.1
  • 8
    • 67649354433 scopus 로고    scopus 로고
    • Periodic orbits and zeta functions
    • Hasselblatt B., and Katok A. (Eds), Elsevier, Amsterdam
    • Pollicott M. Periodic orbits and zeta functions. In: Hasselblatt B., and Katok A. (Eds). Handbook of Dynamical Systems Vol. 1 A (2002), Elsevier, Amsterdam 409-452
    • (2002) Handbook of Dynamical Systems , vol.1 A , pp. 409-452
    • Pollicott, M.1
  • 9
    • 33748538269 scopus 로고    scopus 로고
    • Homoclinic bifurcations, dominated splitting and robust transitivity
    • Hasselblatt B., and Katok A. (Eds), Elsevier, Amsterdam
    • Pujals E., and Sambarino M. Homoclinic bifurcations, dominated splitting and robust transitivity. In: Hasselblatt B., and Katok A. (Eds). Handbook of Dynamical Systems Vol. 1B (2006), Elsevier, Amsterdam 327-378
    • (2006) Handbook of Dynamical Systems , vol.1 B , pp. 327-378
    • Pujals, E.1    Sambarino, M.2
  • 10
    • 0003326377 scopus 로고    scopus 로고
    • An introduction to infinite ergodic theory
    • Amer. Math. Soc.
    • Aaronson J. An introduction to infinite ergodic theory. Mathematical Surveys and Monographs Vol. 50 (1997), Amer. Math. Soc.
    • (1997) Mathematical Surveys and Monographs , vol.50
    • Aaronson, J.1
  • 11
    • 0002256106 scopus 로고
    • F -expansions revisited
    • Recent Advances in Topological Dynamics. Proc. Conf., Yale Univ. in honor of Gustav Arnold Nedlund. New Haven, Conn., 1972, Springer, Berlin
    • Recent Advances in Topological Dynamics. Adler R.L. F -expansions revisited. in honor of Gustav Arnold Nedlund. Proc. Conf., Yale Univ. New Haven, Conn., 1972. Lecture Notes in Math. Vol. 318 (1973), Springer, Berlin 1-5
    • (1973) Lecture Notes in Math. , vol.318 , pp. 1-5
    • Adler, R.L.1
  • 12
    • 0033636267 scopus 로고
    • SRB measures for non-hyperbolic systems with multidimensional expansion
    • Alves J.F. SRB measures for non-hyperbolic systems with multidimensional expansion. Ann. Sci. École Norm. Sup. 33 4 (1900) 1-32
    • (1900) Ann. Sci. École Norm. Sup. , vol.33 , Issue.4 , pp. 1-32
    • Alves, J.F.1
  • 14
    • 0037385190 scopus 로고    scopus 로고
    • On the uniform hyperbolicity of some nonuniformly hyperbolic systems
    • Alves J.F., Araujo V., and Saussol B. On the uniform hyperbolicity of some nonuniformly hyperbolic systems. Proc. Amer. Math. Soc. 131 4 (2003) 1303-1309
    • (2003) Proc. Amer. Math. Soc. , vol.131 , Issue.4 , pp. 1303-1309
    • Alves, J.F.1    Araujo, V.2    Saussol, B.3
  • 15
    • 0034349012 scopus 로고    scopus 로고
    • SRB measures for partially hyperbolic systems whose central direction is mostly expanding
    • Alves J.F., Bonatti C., and Viana M. SRB measures for partially hyperbolic systems whose central direction is mostly expanding. Invent. Math. 140 (2000) 351-398
    • (2000) Invent. Math. , vol.140 , pp. 351-398
    • Alves, J.F.1    Bonatti, C.2    Viana, M.3
  • 16
    • 15944377443 scopus 로고    scopus 로고
    • Markov structures and decay of correlations for non-uniformly expanding maps on compact manifolds of arbitrary dimension
    • Alves J.F., Luzzatto S., and Pinheiro V. Markov structures and decay of correlations for non-uniformly expanding maps on compact manifolds of arbitrary dimension. Electron. Res. Announc. Amer. Math. Soc. 9 (2003) 26-31
    • (2003) Electron. Res. Announc. Amer. Math. Soc. , vol.9 , pp. 26-31
    • Alves, J.F.1    Luzzatto, S.2    Pinheiro, V.3
  • 17
    • 2942688189 scopus 로고
    • Lyapunov exponents and rates of mixing for one-dimensional maps
    • DOI 10.1017/S0143385703000579
    • DOI 10.1017/S0143385703000579. Alves J.F., Luzzatto S., and Pinheiro V. Lyapunov exponents and rates of mixing for one-dimensional maps. Ergodic Theory Dynam. Systems 24 (1904) 637-657
    • (1904) Ergodic Theory Dynam. Systems , vol.24 , pp. 637-657
    • Alves, J.F.1    Luzzatto, S.2    Pinheiro, V.3
  • 19
    • 0035981909 scopus 로고    scopus 로고
    • Statistical stability for robust classes of maps with non-uniform expansion
    • Alves J.F., and Viana M. Statistical stability for robust classes of maps with non-uniform expansion. Er-godic Theory Dynam. Systems 22 (2002) 1-32
    • (2002) Er-godic Theory Dynam. Systems , vol.22 , pp. 1-32
    • Alves, J.F.1    Viana, M.2
  • 20
    • 0035343985 scopus 로고    scopus 로고
    • Infinitely many stochastically stable attractors
    • Araújo V. Infinitely many stochastically stable attractors. Nonlinearity 14 (2001) 583-596
    • (2001) Nonlinearity , vol.14 , pp. 583-596
    • Araújo, V.1
  • 21
    • 67649330739 scopus 로고    scopus 로고
    • V. Araújo, M. Viana and S. Luzzatto, Weak expansion implies stochastic stability, in progress
    • V. Araújo, M. Viana and S. Luzzatto, Weak expansion implies stochastic stability, in progress.
  • 22
    • 0040572571 scopus 로고
    • Propriétés ergodiques des endomorphisms dilatants des variétés compactes
    • (in French)
    • (in French). Avez A. Propriétés ergodiques des endomorphisms dilatants des variétés compactes. C. R. Acad. Sci. Paris Sér. A-B 266 (1968) A610-A612
    • (1968) C. R. Acad. Sci. Paris Sér. A-B , vol.266
    • Avez, A.1
  • 25
    • 0000640307 scopus 로고    scopus 로고
    • Strong stochastic stability and rate of mixing for unimodal maps
    • Baladi V., and Viana M. Strong stochastic stability and rate of mixing for unimodal maps. Ann. Sci. École Norm. Sup. 29 4 (1996) 483-517
    • (1996) Ann. Sci. École Norm. Sup. , vol.29 , Issue.4 , pp. 483-517
    • Baladi, V.1    Viana, M.2
  • 26
    • 21144471502 scopus 로고
    • On the spectra of randomly perturbed expanding maps
    • Baladi V., and Young L.-S. On the spectra of randomly perturbed expanding maps. Comm. Math. Phys. 156 (1993) 355-385
    • (1993) Comm. Math. Phys. , vol.156 , pp. 355-385
    • Baladi, V.1    Young, L.-S.2
  • 27
    • 0347242246 scopus 로고    scopus 로고
    • Lyapunov exponents and smooth ergodic theory
    • Amer. Math. Soc, Providence, RI. 0-8218-2921-1
    • Barreira L., and Pesin Y.B. Lyapunov exponents and smooth ergodic theory. University Lecture Series Vol. 23 (2002), Amer. Math. Soc, Providence, RI. 0-8218-2921-1
    • (2002) University Lecture Series , vol.23
    • Barreira, L.1    Pesin, Y.B.2
  • 29
    • 0001870459 scopus 로고
    • The dynamics of the Hénon map
    • Benedicks M., and Carleson L. The dynamics of the Hénon map. Ann. of Math. 133 (1991) 73-169
    • (1991) Ann. of Math. , vol.133 , pp. 73-169
    • Benedicks, M.1    Carleson, L.2
  • 31
    • 0009181928 scopus 로고
    • What is the ergodic theorem?
    • jstor
    • jstor. Birkhoff G.D. What is the ergodic theorem?. Amer. Math. Monthly 49 (1942) 222-226
    • (1942) Amer. Math. Monthly , vol.49 , pp. 222-226
    • Birkhoff, G.D.1
  • 32
    • 0001300739 scopus 로고
    • Markov partitions for Axiom A diffeomorphisms
    • Bowen R. Markov partitions for Axiom A diffeomorphisms. Amer. J. Math. 92 (1970) 725-741
    • (1970) Amer. J. Math. , vol.92 , pp. 725-741
    • Bowen, R.1
  • 33
    • 0003208028 scopus 로고
    • Equilibrium states and the ergodic theory ofAnosov diffeomorphisms
    • Springer-Verlag, Berlin
    • Bowen R. Equilibrium states and the ergodic theory ofAnosov diffeomorphisms. Lecture Notes in Math. Vol. 470 (1975), Springer-Verlag, Berlin
    • (1975) Lecture Notes in Math. , vol.470
    • Bowen, R.1
  • 34
    • 51249187045 scopus 로고
    • Bernoulli maps of the interval
    • Bowen R. Bernoulli maps of the interval. Israel J. Math. 28 (1977) 161-168
    • (1977) Israel J. Math. , vol.28 , pp. 161-168
    • Bowen, R.1
  • 35
    • 0000098298 scopus 로고
    • Invariant measures for Markov maps of the interval
    • with an afterword by Roy L. Adler and additional comments by Caroline Series
    • with an afterword by Roy L. Adler and additional comments by Caroline Series. Bowen R. Invariant measures for Markov maps of the interval. Comm. Math. Phys. 69 (1979) 1-17
    • (1979) Comm. Math. Phys. , vol.69 , pp. 1-17
    • Bowen, R.1
  • 36
    • 0033444391 scopus 로고    scopus 로고
    • Subshifis on an infinite alphabet
    • Bressaud X. Subshifis on an infinite alphabet. Ergodic Theory Dynam. Systems 19 (1999) 1175-1200
    • (1999) Ergodic Theory Dynam. Systems , vol.19 , pp. 1175-1200
    • Bressaud, X.1
  • 37
    • 0042160387 scopus 로고    scopus 로고
    • Decay of correlations for non-Hölderian dynamics. A coupling approach
    • 19 pp. (electronic)
    • 19 pp. (electronic). Bressaud X., Fernández R., and Galves A. Decay of correlations for non-Hölderian dynamics. A coupling approach. Electron. J. Probab. 4 3 (1999)
    • (1999) Electron. J. Probab. , vol.4 , Issue.3
    • Bressaud, X.1    Fernández, R.2    Galves, A.3
  • 38
    • 0005038888 scopus 로고
    • Topological conditions for the existence of invariant measures for unimodal maps
    • Bruin H. Topological conditions for the existence of invariant measures for unimodal maps. Ergodic Theory Dynam. Systems 14 (1994) 433-451
    • (1994) Ergodic Theory Dynam. Systems , vol.14 , pp. 433-451
    • Bruin, H.1
  • 39
    • 0032395453 scopus 로고    scopus 로고
    • The existence of absolutely continuous invariant measures is not a topological invariant for unimodal maps
    • Bruin H. The existence of absolutely continuous invariant measures is not a topological invariant for unimodal maps. Ergodic Theory Dynam. Systems 18 (1998) 555-565
    • (1998) Ergodic Theory Dynam. Systems , vol.18 , pp. 555-565
    • Bruin, H.1
  • 40
    • 22044437795 scopus 로고    scopus 로고
    • Topological conditions for the existence of absorbing Cantor sets
    • Bruin H. Topological conditions for the existence of absorbing Cantor sets. Trans. Amer. Math. Soc. 350 (1998) 2229-2263
    • (1998) Trans. Amer. Math. Soc. , vol.350 , pp. 2229-2263
    • Bruin, H.1
  • 41
  • 43
    • 0242370750 scopus 로고    scopus 로고
    • Invariant measures exist without a growth condition
    • Bruin H., Shen W., and Strien S.v. Invariant measures exist without a growth condition. Comm. Math. Phys. 241 (2003) 287-306
    • (2003) Comm. Math. Phys. , vol.241 , pp. 287-306
    • Bruin, H.1    Shen, W.2    Strien, S.v.3
  • 44
    • 27844517338 scopus 로고
    • Existence of absolutely continuous invariant probability measures for multi-modal maps
    • Inst. Phys., Bristol
    • Bruin H., and Strien S.v. Existence of absolutely continuous invariant probability measures for multi-modal maps. Global Analysis of Dynamical Systems (1901), Inst. Phys., Bristol 433-447
    • (1901) Global Analysis of Dynamical Systems , pp. 433-447
    • Bruin, H.1    Strien, S.v.2
  • 45
    • 0010671830 scopus 로고
    • On a transformation of the circle
    • (in Russian)
    • (in Russian). Bunimovič L.A. On a transformation of the circle. Mat. Zametki 8 (1970) 205-216
    • (1970) Mat. Zametki , vol.8 , pp. 205-216
    • Bunimovič, L.A.1
  • 47
    • 0040348559 scopus 로고    scopus 로고
    • Absolutely continuous invariant measures for generic multi-dimensional piecewise affine expand-ing maps
    • Discrete dynamical systems
    • Discrete dynamical systems. Buzzi J. Absolutely continuous invariant measures for generic multi-dimensional piecewise affine expand-ing maps. Internat. J. Bifur. Chaos Appl. Sci. Engrg. 9 (1999) 1743-1750
    • (1999) Internat. J. Bifur. Chaos Appl. Sci. Engrg. , vol.9 , pp. 1743-1750
    • Buzzi, J.1
  • 48
    • 0034399121 scopus 로고    scopus 로고
    • Absolutely continuous invariant probability measures for arbitrary expanding piecewise R-analytic mappings of the plane
    • Buzzi J. Absolutely continuous invariant probability measures for arbitrary expanding piecewise R-analytic mappings of the plane. Ergodic Theory Dynam. Systems 20 (2000) 697-708
    • (2000) Ergodic Theory Dynam. Systems , vol.20 , pp. 697-708
    • Buzzi, J.1
  • 49
    • 0035648072 scopus 로고    scopus 로고
    • r maps in higher dimensions
    • r maps in higher dimensions. Comm. Math. Phys. 222 (2001) 495-501
    • (2001) Comm. Math. Phys. , vol.222 , pp. 495-501
    • Buzzi, J.1
  • 50
    • 0012039131 scopus 로고    scopus 로고
    • Thermodynamical formalism for piecewise invertible maps: absolutely continuous invariant measures as equilibrium states
    • (in English, with English and French summaries), Amer. Math. Soc, Providence, RI
    • (in English, with English and French summaries). Buzzi J. Thermodynamical formalism for piecewise invertible maps: absolutely continuous invariant measures as equilibrium states. Smooth ergodic theory and its applications, Seattle, WA, 1999, Proc. Sympos. Pure Math. Vol. 69 (2001), Amer. Math. Soc, Providence, RI 749-783
    • (2001) Smooth ergodic theory and its applications, Seattle, WA, 1999, Proc. Sympos. Pure Math. , vol.69 , pp. 749-783
    • Buzzi, J.1
  • 51
    • 0035608682 scopus 로고    scopus 로고
    • Zeta functions and transfer operators for multidimensional piecewise affine and expanding maps
    • Buzzi J., and Keller G. Zeta functions and transfer operators for multidimensional piecewise affine and expanding maps. Ergodic Theory Dynam. Systems 21 (2001) 689-716
    • (2001) Ergodic Theory Dynam. Systems , vol.21 , pp. 689-716
    • Buzzi, J.1    Keller, G.2
  • 52
    • 0036459262 scopus 로고    scopus 로고
    • Decay of correlations for piecewise invertible maps in higher dimen-sions
    • Buzzi J., and Maume-Deschamps V. Decay of correlations for piecewise invertible maps in higher dimen-sions. Israel J. Math. 131 (2002) 203-220
    • (2002) Israel J. Math. , vol.131 , pp. 203-220
    • Buzzi, J.1    Maume-Deschamps, V.2
  • 53
    • 0039741658 scopus 로고    scopus 로고
    • Conformai measures for multidimensional piecewise invertible maps
    • Buzzi J., Paccaut F., and Schmitt B. Conformai measures for multidimensional piecewise invertible maps. Ergodic Theory Dynam. Systems 21 (2001) 1035-1049
    • (2001) Ergodic Theory Dynam. Systems , vol.21 , pp. 1035-1049
    • Buzzi, J.1    Paccaut, F.2    Schmitt, B.3
  • 54
    • 0242382473 scopus 로고    scopus 로고
    • Uniqueness of equilibrium measures for countable Markov shifts and multidimen-sional piecewise expanding maps
    • Buzzi J., and Sarig O. Uniqueness of equilibrium measures for countable Markov shifts and multidimen-sional piecewise expanding maps. Ergodic Theory Dynam. Systems 23 (2003) 1383-1400
    • (2003) Ergodic Theory Dynam. Systems , vol.23 , pp. 1383-1400
    • Buzzi, J.1    Sarig, O.2
  • 56
    • 0035402350 scopus 로고    scopus 로고
    • 1 expanding map has a singular S-R-B measure
    • DOI 10.1007/s002200100491
    • 1 expanding map has a singular S-R-B measure. Comm. Math. Phys. 221 (2001) 335-349
    • (2001) Comm. Math. Phys. , vol.221 , pp. 335-349
    • Campbell, J.T.1    Quas, A.N.2
  • 57
    • 0242277089 scopus 로고    scopus 로고
    • Non-zero Lyapunov exponents and uniform hyperbolicity
    • Cao Y. Non-zero Lyapunov exponents and uniform hyperbolicity. Nonlinearity 16 (2003) 1473-1479
    • (2003) Nonlinearity , vol.16 , pp. 1473-1479
    • Cao, Y.1
  • 58
    • 33745229911 scopus 로고    scopus 로고
    • A minimum principle for Lyapunov exponents and a higher-dimensional version of a theorem ofMané
    • to appear
    • to appear. Cao Y., Rios I., and Luzzatto S. A minimum principle for Lyapunov exponents and a higher-dimensional version of a theorem ofMané. Quai. Theory Dynam. Systems (2005)
    • (2005) Quai. Theory Dynam. Systems
    • Cao, Y.1    Rios, I.2    Luzzatto, S.3
  • 60
    • 0002525106 scopus 로고
    • Positive Lyapunov exponents and absolute continuity for maps of the interval
    • Collet P., and Eckmann J.-P. Positive Lyapunov exponents and absolute continuity for maps of the interval. Ergodic Theory Dynam. Systems 3 (1983) 13-46
    • (1983) Ergodic Theory Dynam. Systems , vol.3 , pp. 13-46
    • Collet, P.1    Eckmann, J.-P.2
  • 62
    • 0036687708 scopus 로고    scopus 로고
    • Absolutely continuous invariant measures for most piecewise smooth expanding maps
    • Cowieson W.J. Absolutely continuous invariant measures for most piecewise smooth expanding maps. Ergodic Theory Dynam. Systems 22 (2002) 1061-1078
    • (2002) Ergodic Theory Dynam. Systems , vol.22 , pp. 1061-1078
    • Cowieson, W.J.1
  • 64
    • 26044462766 scopus 로고    scopus 로고
    • Decay of correlations for non-Hölder observables for one-dimensional expanding Lorenzlike maps
    • to appear
    • to appear. Diaz-Ordaz K. Decay of correlations for non-Hölder observables for one-dimensional expanding Lorenzlike maps. Discrete Contin. Dynam. Systems (2005)
    • (2005) Discrete Contin. Dynam. Systems
    • Diaz-Ordaz, K.1
  • 65
    • 0032389434 scopus 로고    scopus 로고
    • On decay of correlations in Anosov flows
    • Dolgopyat D. On decay of correlations in Anosov flows. Ann. of Math. 147 2 (1998) 357-390
    • (1998) Ann. of Math. , vol.147 , Issue.2 , pp. 357-390
    • Dolgopyat, D.1
  • 66
    • 0032333778 scopus 로고    scopus 로고
    • Prevalence of rapid mixing in hyperbolic flows
    • Dolgopyat D. Prevalence of rapid mixing in hyperbolic flows. Ergodic Theory Dynam. Systems 18 (1998) 1097-1114
    • (1998) Ergodic Theory Dynam. Systems , vol.18 , pp. 1097-1114
    • Dolgopyat, D.1
  • 67
    • 0034349951 scopus 로고    scopus 로고
    • On dynamics of mostly contracting diffeomorphisms
    • Dolgopyat D. On dynamics of mostly contracting diffeomorphisms. Comm. Math. Phys. 213 (2000) 181-201
    • (2000) Comm. Math. Phys. , vol.213 , pp. 181-201
    • Dolgopyat, D.1
  • 68
    • 0001372710 scopus 로고
    • A common property of number systems
    • (in Russian)
    • (in Russian). Gel'fond A.O. A common property of number systems. Izv. Akad. Nauk SSSR Ser. Mat. 23 (1959) 809-814
    • (1959) Izv. Akad. Nauk SSSR Ser. Mat. , vol.23 , pp. 809-814
    • Gel'fond, A.O.1
  • 70
    • 84974325811 scopus 로고
    • 1 par morceaux de l'intervalle, sans probabilité absolument continue invariante
    • (in French, with English summary)
    • 1 par morceaux de l'intervalle, sans probabilité absolument continue invariante. Ergodic Theory Dynam. Systems 9 (1989) 101-113
    • (1989) Ergodic Theory Dynam. Systems , vol.9 , pp. 101-113
    • Góra, P.1    Schmitt, B.2
  • 72
    • 1842425473 scopus 로고    scopus 로고
    • Sharp polynomial estimates for the decay of correlations
    • Gouëzel S. Sharp polynomial estimates for the decay of correlations. Israel J. Math. 139 (2004) 29-65
    • (2004) Israel J. Math. , vol.139 , pp. 29-65
    • Gouëzel, S.1
  • 74
    • 0031530948 scopus 로고    scopus 로고
    • Generic hyperbolicity in the logistic family
    • Graczyk J., and Świtek G. Generic hyperbolicity in the logistic family. Ann. of Math. 146 2 (1997) 1-52
    • (1997) Ann. of Math. , vol.146 , Issue.2 , pp. 1-52
    • Graczyk, J.1    Świtek, G.2
  • 75
    • 0011829596 scopus 로고
    • In general a measure preserving transformation is mixing
    • Halmos P.R. In general a measure preserving transformation is mixing. Ann. of Math. 45 2 (1944) 786-792
    • (1944) Ann. of Math. , vol.45 , Issue.2 , pp. 786-792
    • Halmos, P.R.1
  • 76
    • 0000819591 scopus 로고
    • Ergodic properties of invariant measures for piecewise monotonic transforma-tions
    • Hofbauer F., and Keller G. Ergodic properties of invariant measures for piecewise monotonic transforma-tions. Math. Z. 180 (1982) 119-140
    • (1982) Math. Z. , vol.180 , pp. 119-140
    • Hofbauer, F.1    Keller, G.2
  • 77
    • 13444304315 scopus 로고    scopus 로고
    • Slowly mixing systems and intermittency maps
    • Holland M. Slowly mixing systems and intermittency maps. Ergodic Theory Dynam. Systems 25 1 (2005) 133-159
    • (2005) Ergodic Theory Dynam. Systems , vol.25 , Issue.1 , pp. 133-159
    • Holland, M.1
  • 78
    • 67649368294 scopus 로고
    • On the existence of a mixing measure
    • Holladay J.C. On the existence of a mixing measure. Proc. Amer. Math. Soc. 8 (1957) 887-893
    • (1957) Proc. Amer. Math. Soc. , vol.8 , pp. 887-893
    • Holladay, J.C.1
  • 79
    • 84968505693 scopus 로고
    • Theory of measure and invariant integrals
    • Hopf E. Theory of measure and invariant integrals. Trans. Amer. Math. Soc. 34 (1932) 373-393
    • (1932) Trans. Amer. Math. Soc. , vol.34 , pp. 373-393
    • Hopf, E.1
  • 80
    • 0000683114 scopus 로고
    • Statistik der geodätischen Linien in Mannigfaltigkeiten negativer Krümmung
    • (in German)
    • (in German). Hopf E. Statistik der geodätischen Linien in Mannigfaltigkeiten negativer Krümmung. Ber. Verh. Sächs. Akad. Wiss. Leipzig 91 (1939) 261-304
    • (1939) Ber. Verh. Sächs. Akad. Wiss. Leipzig , vol.91 , pp. 261-304
    • Hopf, E.1
  • 82
    • 2442534074 scopus 로고    scopus 로고
    • Decay of correlations for piecewise smooth maps with indifferent fixed points
    • Hu H. Decay of correlations for piecewise smooth maps with indifferent fixed points. Ergodic Theory Dynam. Systems 24 (2004) 495-524
    • (2004) Ergodic Theory Dynam. Systems , vol.24 , pp. 495-524
    • Hu, H.1
  • 83
    • 84974325915 scopus 로고
    • Nonexistence of SBR measures for some diffeomorphisms that are "almost Anosov"
    • Hu H.Y., and Young L.-S. Nonexistence of SBR measures for some diffeomorphisms that are "almost Anosov". Ergodic Theory Dynam. Systems 15 (1995) 67-76
    • (1995) Ergodic Theory Dynam. Systems , vol.15 , pp. 67-76
    • Hu, H.Y.1    Young, L.-S.2
  • 84
    • 0033212052 scopus 로고    scopus 로고
    • Renewal sequences and intermittency
    • Isola S. Renewal sequences and intermittency. J. Statist. Phys. 97 (1999) 263-280
    • (1999) J. Statist. Phys. , vol.97 , pp. 263-280
    • Isola, S.1
  • 85
    • 0012062906 scopus 로고
    • Topological and metric properties of one-dimensional endomorphisms
    • Jakobson M.V. Topological and metric properties of one-dimensional endomorphisms. Sov. Math. Dokl. 19 (1978) 1452-1456
    • (1978) Sov. Math. Dokl. , vol.19 , pp. 1452-1456
    • Jakobson, M.V.1
  • 86
    • 0002053804 scopus 로고
    • Absolutely continuous invariant measures for one-parameter families of one-dimensional maps
    • Jakobson M.V. Absolutely continuous invariant measures for one-parameter families of one-dimensional maps. Comm. Math. Phys. 81 (1981) 39-88
    • (1981) Comm. Math. Phys. , vol.81 , pp. 39-88
    • Jakobson, M.V.1
  • 87
    • 33745378706 scopus 로고    scopus 로고
    • Piecewise smooth maps with absolutely continuous invariant measures and uniformly scaled Markov partitions
    • Jakobson M.V. Piecewise smooth maps with absolutely continuous invariant measures and uniformly scaled Markov partitions. Proc. Sympos. Pure Math. 69 (2001) 825-881
    • (2001) Proc. Sympos. Pure Math. , vol.69 , pp. 825-881
    • Jakobson, M.V.1
  • 88
    • 84959302337 scopus 로고    scopus 로고
    • Parameter choice for families of maps with many critical points
    • Jakobson M.V. Parameter choice for families of maps with many critical points. Modern Dynam. Systems Appl. (2004)
    • (2004) Modern Dynam. Systems Appl.
    • Jakobson, M.V.1
  • 89
    • 67649339025 scopus 로고
    • On rapidly mixing transformations and an application to continued fractions
    • Kac M., and Kesten H. On rapidly mixing transformations and an application to continued fractions. Bull. Amer. Math. Soc. 64 (1958) 283
    • (1958) Bull. Amer. Math. Soc. , vol.64 , pp. 283
    • Kac, M.1    Kesten, H.2
  • 90
    • 67649339025 scopus 로고
    • On rapidly mixing transformations and an application to continued fractions
    • correction
    • correction. Kac M., and Kesten H. On rapidly mixing transformations and an application to continued fractions. Bull. Amer. Math. Soc. 65 (1958) 67
    • (1958) Bull. Amer. Math. Soc. , vol.65 , pp. 67
    • Kac, M.1    Kesten, H.2
  • 91
    • 0000983845 scopus 로고
    • Ergodicité et mesures invariantes pour les transformations dilatantes par morceaux d'une ré-gion bornée du plan
    • (in French, with English summary)
    • (in French, with English summary). Keller G. Ergodicité et mesures invariantes pour les transformations dilatantes par morceaux d'une ré-gion bornée du plan. C. R. Acad. Sci. Paris Sér. A-B 289 (1979) A625-A627
    • (1979) C. R. Acad. Sci. Paris Sér. A-B , vol.289
    • Keller, G.1
  • 92
    • 0007436260 scopus 로고
    • Un théorème de la limite centrale pour une classe de transformations monotones par morceaux
    • (in French, with English summary)
    • (in French, with English summary). Keller G. Un théorème de la limite centrale pour une classe de transformations monotones par morceaux. C. R. Acad. Sci. Paris Sér. A-B 291 (1980) A155-A158
    • (1980) C. R. Acad. Sci. Paris Sér. A-B , vol.291
    • Keller, G.1
  • 93
    • 0002160620 scopus 로고
    • Spectraltheory zeta functions and the distribution of periodic points for Collet-Eckmann maps
    • Keller G., and Nowicki T. Spectraltheory zeta functions and the distribution of periodic points for Collet-Eckmann maps. Comm. Math. Phys. 149 (1992) 31-69
    • (1992) Comm. Math. Phys. , vol.149 , pp. 31-69
    • Keller, G.1    Nowicki, T.2
  • 94
    • 0034310140 scopus 로고    scopus 로고
    • Getting rid of the negative Schwarzian derivative condition
    • Kozlovski O.S. Getting rid of the negative Schwarzian derivative condition. Ann. of Math. 152 2 (2000) 743-762
    • (2000) Ann. of Math. , vol.152 , Issue.2 , pp. 743-762
    • Kozlovski, O.S.1
  • 97
    • 0002305647 scopus 로고
    • On invariant measures for expanding differentiable mappings
    • Krzyzewski K., and Szlenk W. On invariant measures for expanding differentiable mappings. Studia Math. 33 (1969) 83-92
    • (1969) Studia Math. , vol.33 , pp. 83-92
    • Krzyzewski, K.1    Szlenk, W.2
  • 98
    • 34250438265 scopus 로고
    • Invariant measures and functional equations
    • Lasota A. Invariant measures and functional equations. Aequationes Math. 9 (1973) 193-200
    • (1973) Aequationes Math. , vol.9 , pp. 193-200
    • Lasota, A.1
  • 99
    • 84966227493 scopus 로고
    • On the existence of invariant measures for piecewise monotonie transformations
    • 1974
    • 1974. Lasota A., and Yorke J.A. On the existence of invariant measures for piecewise monotonie transformations. Trans. Amer. Math. Soc. 186 (1973) 481-488
    • (1973) Trans. Amer. Math. Soc. , vol.186 , pp. 481-488
    • Lasota, A.1    Yorke, J.A.2
  • 100
    • 21844485876 scopus 로고
    • Decay of correlations for piecewise expanding maps
    • Liverani C. Decay of correlations for piecewise expanding maps. J. Statist. Phys. 78 (1995) 1111-1129
    • (1995) J. Statist. Phys. , vol.78 , pp. 1111-1129
    • Liverani, C.1
  • 101
    • 0000345142 scopus 로고
    • Decay of correlations
    • Liverani C. Decay of correlations. Ann. of Math. 142 2 (1995) 239-301
    • (1995) Ann. of Math. , vol.142 , Issue.2 , pp. 239-301
    • Liverani, C.1
  • 103
    • 0032357405 scopus 로고    scopus 로고
    • Conformai measure and decay of correlation for covering weighted systems
    • Liverani C., Saussol B., and Vaienti S. Conformai measure and decay of correlation for covering weighted systems. Ergodic Theory Dynam. Systems 18 (1998) 1399-1420
    • (1998) Ergodic Theory Dynam. Systems , vol.18 , pp. 1399-1420
    • Liverani, C.1    Saussol, B.2    Vaienti, S.3
  • 104
    • 2442454708 scopus 로고    scopus 로고
    • Bounded recurrence of critical points and Jakobson's theorem
    • The Mandelbrot Set, Theme and Variations, Cambridge Univ. Press, Cambridge
    • Luzzatto S. Bounded recurrence of critical points and Jakobson's theorem. The Mandelbrot Set, Theme and Variations. London Math. Soc. Lecture Note Ser. Vol. 274 (2000), Cambridge Univ. Press, Cambridge 173-210
    • (2000) London Math. Soc. Lecture Note Ser. , vol.274 , pp. 173-210
    • Luzzatto, S.1
  • 105
    • 67649346944 scopus 로고    scopus 로고
    • Mixing properties of one-dimensional Lorenz-like maps with critical points and discontinuities with infinite derivative
    • to appear
    • to appear. Luzzatto S., Holland M., and Diaz-Ordaz K. Mixing properties of one-dimensional Lorenz-like maps with critical points and discontinuities with infinite derivative. Stochastics and Dynamics (2005)
    • (2005) Stochastics and Dynamics
    • Luzzatto, S.1    Holland, M.2    Diaz-Ordaz, K.3
  • 106
    • 67649315102 scopus 로고    scopus 로고
    • S. Luzzatto and F. Sanchez-Salas, Markov structures for nonuniformly hyperbolic surface dijfeomorphisms, in progress
    • S. Luzzatto and F. Sanchez-Salas, Markov structures for nonuniformly hyperbolic surface dijfeomorphisms, in progress.
  • 112
    • 67649368293 scopus 로고    scopus 로고
    • Decay of correlations for non-Hölder continuous observables
    • to appear
    • to appear. Lynch V. Decay of correlations for non-Hölder continuous observables. Discrete Contin. Dynam. Systems (2005)
    • (2005) Discrete Contin. Dynam. Systems
    • Lynch, V.1
  • 113
    • 0001057166 scopus 로고    scopus 로고
    • Dynamics of quadratic polynomials. I, II
    • Lyubich M. Dynamics of quadratic polynomials. I, II. Acta Math. 178 (1997) 185-247
    • (1997) Acta Math. , vol.178 , pp. 185-247
    • Lyubich, M.1
  • 114
    • 0001057166 scopus 로고    scopus 로고
    • Dynamics of quadratic polynomials. I, II
    • Lyubich M. Dynamics of quadratic polynomials. I, II. Acta Math. 178 (1997) 247-297
    • (1997) Acta Math. , vol.178 , pp. 247-297
    • Lyubich, M.1
  • 116
    • 34250112903 scopus 로고
    • sinks and measure in one-dimensional dynamics
    • 495-524
    • Ma≈nié R. sinks and measure in one-dimensional dynamics. Comm. Math. Phys. 100 (1985) 495-524
    • (1985) Comm. Math. Phys. , vol.100
    • Manié, R.1
  • 117
    • 34250254669 scopus 로고
    • Intermittent transition to turbulence in dissipative dynamical systems
    • Manneville P., and Pomeau Y. Intermittent transition to turbulence in dissipative dynamical systems. Comm. Math. Phys. 74 (1980) 189-197
    • (1980) Comm. Math. Phys. , vol.74 , pp. 189-197
    • Manneville, P.1    Pomeau, Y.2
  • 118
    • 0035631263 scopus 로고    scopus 로고
    • Correlation decay for Markov maps on a countable state space
    • Maume-Deschamps V. Correlation decay for Markov maps on a countable state space. Ergodic Theory Dynam. Systems 21 (2001) 165-196
    • (2001) Ergodic Theory Dynam. Systems , vol.21 , pp. 165-196
    • Maume-Deschamps, V.1
  • 119
    • 23044528342 scopus 로고    scopus 로고
    • Projective metrics and mixing properties on towers
    • (electronic)
    • (electronic). Maume-Deschamps V. Projective metrics and mixing properties on towers. Trans. Amer. Math. Soc. 353 (2001) 3371-3389
    • (2001) Trans. Amer. Math. Soc. , vol.353 , pp. 3371-3389
    • Maume-Deschamps, V.1
  • 120
    • 84968502673 scopus 로고
    • One-dimensional dynamics: The Schwarzian derivative and beyond
    • Melo W.d., and Strien S.v. One-dimensional dynamics: The Schwarzian derivative and beyond. Bull. Amer. Math. Soc. (N.S.) 18 (1988) 159-162
    • (1988) Bull. Amer. Math. Soc. (N.S.) , vol.18 , pp. 159-162
    • Melo, W.d.1    Strien, S.v.2
  • 122
    • 51249183577 scopus 로고
    • Absolutely continuous measures for certain maps of an interval
    • Misiurewicz M. Absolutely continuous measures for certain maps of an interval. Inst. Hautes Études Sci. Publ. Math. 53 (1981) 17-51
    • (1981) Inst. Hautes Études Sci. Publ. Math. , vol.53 , pp. 17-51
    • Misiurewicz, M.1
  • 123
    • 84974201081 scopus 로고
    • A positive Liapunov exponent for the critical value of an S-unimodal mapping implies uniform hyperbolicity
    • Nowicki T. A positive Liapunov exponent for the critical value of an S-unimodal mapping implies uniform hyperbolicity. Ergodic Theory Dynam. Systems 8 (1988) 425-435
    • (1988) Ergodic Theory Dynam. Systems , vol.8 , pp. 425-435
    • Nowicki, T.1
  • 124
    • 0040163957 scopus 로고    scopus 로고
    • Topological invariance of the Collet-Eckmann property for S-unimodal maps
    • Nowicki T., and Przytycki F. Topological invariance of the Collet-Eckmann property for S-unimodal maps. Fund. Math. 155 (1998) 33-43
    • (1998) Fund. Math. , vol.155 , pp. 33-43
    • Nowicki, T.1    Przytycki, F.2
  • 125
    • 0032382986 scopus 로고    scopus 로고
    • Non-uniform hyperbolicity and universal bounds for S-unimodal maps
    • Nowicki T., and Sands D. Non-uniform hyperbolicity and universal bounds for S-unimodal maps. Invent. Math. 132 (1998) 633-680
    • (1998) Invent. Math. , vol.132 , pp. 633-680
    • Nowicki, T.1    Sands, D.2
  • 126
    • 0040977663 scopus 로고
    • 2 unimodal maps satisfying the Collet-Eckmann conditions
    • 2 unimodal maps satisfying the Collet-Eckmann conditions. Invent. Math. 93 (1988) 619-635
    • (1988) Invent. Math. , vol.93 , pp. 619-635
    • Nowicki, T.1    Strien, S.v.2
  • 127
    • 0002046772 scopus 로고
    • Invariant measures exist under a summability condition for unimodal maps
    • Nowicki T., and Strien S.v. Invariant measures exist under a summability condition for unimodal maps. Invent. Math. 105 (1991) 123-136
    • (1991) Invent. Math. , vol.105 , pp. 123-136
    • Nowicki, T.1    Strien, S.v.2
  • 128
    • 0010564057 scopus 로고
    • On the β-expansions of real numbers
    • (in English, with Russian summary)
    • (in English, with Russian summary). Parry W. On the β-expansions of real numbers. Acta Math. Acad. Sci. Hungar. 11 (1960) 401-416
    • (1960) Acta Math. Acad. Sci. Hungar. , vol.11 , pp. 401-416
    • Parry, W.1
  • 129
    • 0038862681 scopus 로고
    • On the exponential decay of correlation functions
    • Penrose O., and Lebowitz J.L. On the exponential decay of correlation functions. Comm. Math. Phys. 39 (1974) 165-184
    • (1974) Comm. Math. Phys. , vol.39 , pp. 165-184
    • Penrose, O.1    Lebowitz, J.L.2
  • 130
    • 0001022947 scopus 로고
    • Exponential mixing in C-systems
    • (in Russian)
    • (in Russian). Perekrest V.T. Exponential mixing in C-systems. Uspekhi Mat. Nauk 29 (1974) 181-182
    • (1974) Uspekhi Mat. Nauk , vol.29 , pp. 181-182
    • Perekrest, V.T.1
  • 131
    • 84927987560 scopus 로고
    • Families of invariant manifolds corresponding to non-zero characteristic exponents
    • Pesin Ya. Families of invariant manifolds corresponding to non-zero characteristic exponents. Math. USSR Izv. 10 (1976) 1261-1302
    • (1976) Math. USSR Izv. , vol.10 , pp. 1261-1302
    • Pesin, Ya.1
  • 132
    • 84961291543 scopus 로고
    • Characteristic Lyapunov exponents and smooth ergodic theory
    • Pesin Ya.B. Characteristic Lyapunov exponents and smooth ergodic theory. Russian Math. Surveys 324 (1977) 55-114
    • (1977) Russian Math. Surveys , vol.324 , pp. 55-114
    • Pesin, Ya.B.1
  • 133
    • 51249185195 scopus 로고
    • First return map and invariant measures
    • Pianigiani G. First return map and invariant measures. Israel J. Math. 35 (1980) 32-48
    • (1980) Israel J. Math. , vol.35 , pp. 32-48
    • Pianigiani, G.1
  • 134
    • 0035531640 scopus 로고    scopus 로고
    • Statistical properties of maps with indifferent periodic points
    • Pollicott M., and Yuri M. Statistical properties of maps with indifferent periodic points. Comm. Math. Phys. 217 (2001) 503-520
    • (2001) Comm. Math. Phys. , vol.217 , pp. 503-520
    • Pollicott, M.1    Yuri, M.2
  • 135
    • 0037214440 scopus 로고    scopus 로고
    • Equivalence and topological invariance of conditions for non-uniform hyperbolicity in the iteration of rational maps
    • Przytycki F., Rivera-Letelier J., and Smirnov S. Equivalence and topological invariance of conditions for non-uniform hyperbolicity in the iteration of rational maps. Invent. Math. 151 (2003) 29-63
    • (2003) Invent. Math. , vol.151 , pp. 29-63
    • Przytycki, F.1    Rivera-Letelier, J.2    Smirnov, S.3
  • 136
    • 0032428496 scopus 로고    scopus 로고
    • Porosity of Collet-Eckmann Julia sets
    • Przytycki F., and Rohde S. Porosity of Collet-Eckmann Julia sets. Fund. Math. 155 (1998) 189-199
    • (1998) Fund. Math. , vol.155 , pp. 189-199
    • Przytycki, F.1    Rohde, S.2
  • 138
    • 0007033618 scopus 로고    scopus 로고
    • Most expanding maps have no absolutely continuous invariant measure
    • Quas A.N. Most expanding maps have no absolutely continuous invariant measure. Studia Math. 134 (1999) 69-78
    • (1999) Studia Math. , vol.134 , pp. 69-78
    • Quas, A.N.1
  • 139
    • 0040341424 scopus 로고
    • Representations for real numbers and their ergodic properties
    • Rényi A. Representations for real numbers and their ergodic properties. Acta Math. Acad. Sci. Hungar. 8 (1957) 477-493
    • (1957) Acta Math. Acad. Sci. Hungar. , vol.8 , pp. 477-493
    • Rényi, A.1
  • 140
    • 0003186994 scopus 로고
    • A "general" measure-preserving transformation is not mixing
    • (in Russian)
    • (in Russian). Rohlin V. A "general" measure-preserving transformation is not mixing. Doklady Akad. Nauk SSSR (N.S.) 60 (1948) 349-351
    • (1948) Doklady Akad. Nauk SSSR (N.S.) , vol.60 , pp. 349-351
    • Rohlin, V.1
  • 141
    • 0002605356 scopus 로고
    • A central limit theorem and a strong mixing condition
    • Rosenblatt M. A central limit theorem and a strong mixing condition. Proc. Nat. Acad. Sci. USA 42 (1956) 43-47
    • (1956) Proc. Nat. Acad. Sci. USA , vol.42 , pp. 43-47
    • Rosenblatt, M.1
  • 142
    • 0000333996 scopus 로고
    • Statistical mechanics of a one-dimensional lattice gas
    • Ruelle D. Statistical mechanics of a one-dimensional lattice gas. Comm. Math. Phys. 9 (1968) 267-278
    • (1968) Comm. Math. Phys. , vol.9 , pp. 267-278
    • Ruelle, D.1
  • 143
    • 0000809231 scopus 로고
    • A measure associated with axiom-A attractors
    • Ruelle D. A measure associated with axiom-A attractors. Amer. J. Math. 98 (1976) 619-654
    • (1976) Amer. J. Math. , vol.98 , pp. 619-654
    • Ruelle, D.1
  • 144
    • 0002897510 scopus 로고
    • Applications conservant une mesure absolument continue par rapport à dx sur [0,1]
    • (in French, with English summary)
    • (in French, with English summary). Ruelle D. Applications conservant une mesure absolument continue par rapport à dx sur [0,1]. Comm. Math. Phys. 55 (1977) 47-51
    • (1977) Comm. Math. Phys. , vol.55 , pp. 47-51
    • Ruelle, D.1
  • 145
    • 0000320029 scopus 로고
    • Characteristic exponents and invariant manifolds in Hilbert space
    • Ruelle D. Characteristic exponents and invariant manifolds in Hilbert space. Ann. of Math. 115 2 (1982) 243-290
    • (1982) Ann. of Math. , vol.115 , Issue.2 , pp. 243-290
    • Ruelle, D.1
  • 146
    • 0001836914 scopus 로고
    • Bounded variation and invariant measures
    • Rychlik M. Bounded variation and invariant measures. Studia Math. 76 (1983) 69-80
    • (1983) Studia Math. , vol.76 , pp. 69-80
    • Rychlik, M.1
  • 147
    • 0001956838 scopus 로고
    • Another proof of Jakobson's theorem and related results
    • Rychlik M.R. Another proof of Jakobson's theorem and related results. Ergodic Theory Dynam. Systems 8 (1988) 93-109
    • (1988) Ergodic Theory Dynam. Systems , vol.8 , pp. 93-109
    • Rychlik, M.R.1
  • 148
    • 0346283253 scopus 로고    scopus 로고
    • Dimension of Markov towers for non uniformly expanding one-dimensional systems
    • Sánchez-Salas F.J. Dimension of Markov towers for non uniformly expanding one-dimensional systems. Discrete Contin. Dynam. Systems 9 (2003) 1447-1464
    • (2003) Discrete Contin. Dynam. Systems , vol.9 , pp. 1447-1464
    • Sánchez-Salas, F.J.1
  • 150
    • 0036027231 scopus 로고    scopus 로고
    • Subexponential decay of correlations
    • Sarig O. Subexponential decay of correlations. Invent. Math. 150 (2002) 629-653
    • (2002) Invent. Math. , vol.150 , pp. 629-653
    • Sarig, O.1
  • 151
    • 0034366519 scopus 로고    scopus 로고
    • Absolutely continuous invariant measures for multidimensional expanding maps
    • Saussol B. Absolutely continuous invariant measures for multidimensional expanding maps. Israel J. Math. 116 (2000) 223-248
    • (2000) Israel J. Math. , vol.116 , pp. 223-248
    • Saussol, B.1
  • 152
    • 2342461693 scopus 로고    scopus 로고
    • Dimension of weakly expanding points for quadratic maps
    • Senti S. Dimension of weakly expanding points for quadratic maps. Bull. Soc. Math. France 131 (2003) 399-420
    • (2003) Bull. Soc. Math. France , vol.131 , pp. 399-420
    • Senti, S.1
  • 153
    • 67649377690 scopus 로고    scopus 로고
    • 2 density of Axiom A
    • Preprint
    • 2 density of Axiom A, Preprint.
    • Shen, W.1
  • 154
    • 33745351916 scopus 로고
    • Windows of attraction of the logistic map
    • Batschuns, 1989, World Scientific, River Edge, NJ
    • Simó C., and Tatjer J.C. Windows of attraction of the logistic map. European Conference on Iteration Theory. Batschuns, 1989 (1991), World Scientific, River Edge, NJ 335-342
    • (1991) European Conference on Iteration Theory , pp. 335-342
    • Simó, C.1    Tatjer, J.C.2
  • 155
    • 0002131294 scopus 로고
    • Markov partitions and U-diffeomorphisms
    • (in Russian)
    • (in Russian). Sinai Ja.G. Markov partitions and U-diffeomorphisms. Funkcional. Anal i Priložen. 2 (1968) 64-89
    • (1968) Funkcional. Anal i Priložen. , vol.2 , pp. 64-89
    • Sinai, Ja.G.1
  • 156
    • 84956071330 scopus 로고
    • Gibbs measures in ergodic theory
    • (in Russian)
    • (in Russian). Sinai Ja.G. Gibbs measures in ergodic theory. Uspekhi Mat. Nauk 27 (1972) 21-64
    • (1972) Uspekhi Mat. Nauk , vol.27 , pp. 21-64
    • Sinai, Ja.G.1
  • 157
    • 51249181565 scopus 로고
    • Transformations on [0, 1] with infinite invariant measures
    • Thaler M. Transformations on [0, 1] with infinite invariant measures. Israel J. Math. 46 (1983) 67-96
    • (1983) Israel J. Math. , vol.46 , pp. 67-96
    • Thaler, M.1
  • 158
    • 0001748121 scopus 로고
    • Positive Lyapunov exponent for generic one-parameter families of unimodal maps
    • Thieullen Ph., Tresser C., and Young L.-S. Positive Lyapunov exponent for generic one-parameter families of unimodal maps. J. Anal. Math. 64 (1994) 121-172
    • (1994) J. Anal. Math. , vol.64 , pp. 121-172
    • Thieullen, Ph.1    Tresser, C.2    Young, L.-S.3
  • 159
    • 0033457439 scopus 로고    scopus 로고
    • Positive exponent in families with flat critical point
    • Thunberg H. Positive exponent in families with flat critical point. Ergodic Theory Dynam. Systems 19 (1999) 767-807
    • (1999) Ergodic Theory Dynam. Systems , vol.19 , pp. 767-807
    • Thunberg, H.1
  • 160
    • 84972530193 scopus 로고
    • A proof of Benedicks-Carleson-Jacobson theorem
    • Tsujii M. A proof of Benedicks-Carleson-Jacobson theorem. Tokyo J. Math. 16 (1993) 295-310
    • (1993) Tokyo J. Math. , vol.16 , pp. 295-310
    • Tsujii, M.1
  • 161
    • 0001132718 scopus 로고
    • Positive Lyapunov exponents in families of one-dimensional dynamical systems
    • Tsujii M. Positive Lyapunov exponents in families of one-dimensional dynamical systems. Invent. Math. 111 (1993) 113-137
    • (1993) Invent. Math. , vol.111 , pp. 113-137
    • Tsujii, M.1
  • 162
    • 0034367358 scopus 로고    scopus 로고
    • Piecewise expanding maps on the plane with singular ergodic properties
    • Tsujii M. Piecewise expanding maps on the plane with singular ergodic properties. Ergodic Theory Dy-nam. Systems 20 (2000) 1851-1857
    • (2000) Ergodic Theory Dy-nam. Systems , vol.20 , pp. 1851-1857
    • Tsujii, M.1
  • 163
    • 0035586852 scopus 로고    scopus 로고
    • Absolutely continuous invariant measures for expanding piecewise linear maps
    • Tsujii M. Absolutely continuous invariant measures for expanding piecewise linear maps. Invent. Math. 143 (2001) 349-373
    • (2001) Invent. Math. , vol.143 , pp. 349-373
    • Tsujii, M.1
  • 164
    • 0001591606 scopus 로고
    • On combination of stochastic and deterministic processes
    • Ulam S., and Neumann J.v. On combination of stochastic and deterministic processes. Bull. Amer. Math. Soc. 53 (1947) 1120
    • (1947) Bull. Amer. Math. Soc. , vol.53 , pp. 1120
    • Ulam, S.1    Neumann, J.v.2
  • 165
  • 166
    • 0003257107 scopus 로고    scopus 로고
    • Stochastic dynamics of deterministic systems
    • IMPA, Rio de Janeiro
    • Viana M. Stochastic dynamics of deterministic systems. Lecture Notes XXI Braz. Math. Colloq. (1997), IMPA, Rio de Janeiro
    • (1997) Lecture Notes XXI Braz. Math. Colloq.
    • Viana, M.1
  • 169
    • 84974186249 scopus 로고
    • Stochastic stability of hyperbolic attractors
    • Young L.-S. Stochastic stability of hyperbolic attractors. Ergodic Theory Dynam. Systems 6 (1986) 311-319
    • (1986) Ergodic Theory Dynam. Systems , vol.6 , pp. 311-319
    • Young, L.-S.1
  • 170
    • 0001470078 scopus 로고
    • Decay of correlations for certain quadratic maps
    • Young L.-S. Decay of correlations for certain quadratic maps. Comm. Math. Phys. 146 (1992) 123-138
    • (1992) Comm. Math. Phys. , vol.146 , pp. 123-138
    • Young, L.-S.1
  • 171
    • 0003005736 scopus 로고
    • Ergodic theory of differentiable dynamical systems
    • Hiller0d, 1993. Real and Complex Dynamical Systems, Kluwer Academic, Dordrecht
    • Hiller0d, 1993. Young L.-S. Ergodic theory of differentiable dynamical systems. Real and Complex Dynamical Systems. NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci. Vol. 464 (1995), Kluwer Academic, Dordrecht 293-336
    • (1995) NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci. , vol.464 , pp. 293-336
    • Young, L.-S.1
  • 172
    • 0032348050 scopus 로고    scopus 로고
    • Statistical properties of dynamical systems with some hyperbolicity
    • Young L.-S. Statistical properties of dynamical systems with some hyperbolicity. Ann. of Math. 147 2 (1998) 585-650
    • (1998) Ann. of Math. , vol.147 , Issue.2 , pp. 585-650
    • Young, L.-S.1
  • 173
    • 0001396372 scopus 로고    scopus 로고
    • Recurrence times and rates of mixing
    • Young L.-S. Recurrence times and rates of mixing. Israel J. Math. 110 (1999) 153-188
    • (1999) Israel J. Math. , vol.110 , pp. 153-188
    • Young, L.-S.1


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