메뉴 건너뛰기




Volumn 147, Issue 3, 1998, Pages 585-650

Statistical properties of dynamical systems with some hyperbolicity

(1)  Young, Lai Sang a  

a NONE

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0032348050     PISSN: 0003486X     EISSN: None     Source Type: Journal    
DOI: 10.2307/120960     Document Type: Article
Times cited : (699)

References (45)
  • 2
    • 0001870459 scopus 로고
    • The dynamics of the Hénon map
    • _, The dynamics of the Hénon map, Ann. of Math. 133 (1991), 73-169.
    • (1991) Ann. of Math. , vol.133 , pp. 73-169
  • 3
    • 84971895467 scopus 로고
    • Absolutely continuous invariant measures and random perturbations for certain one-dimensional maps
    • M. BENEDICKS and L.-S. YOUNG, Absolutely continuous invariant measures and random perturbations for certain one-dimensional maps, Ergod. Th. & Dynam. Sys. 12 (1992), 13-37.
    • (1992) Ergod. Th. & Dynam. Sys. , vol.12 , pp. 13-37
    • Benedicks, M.1    Young, L.-S.2
  • 4
    • 33845317713 scopus 로고
    • SBR measures for certain Hénon maps
    • _, SBR measures for certain Hénon maps, Invent. Math. 112 (1993), 541-576.
    • (1993) Invent. Math. , vol.112 , pp. 541-576
  • 6
    • 85009367586 scopus 로고
    • Equilibrium states and the ergodic theory of anosov diffeomorphisms
    • [B] R. BOWEN, Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms, Springer Lecture Notes in Math. 470 (1975).
    • (1975) Springer Lecture Notes in Math. , vol.470
    • Bowen, R.1
  • 7
    • 0002031610 scopus 로고
    • Markov partitions for two-dimensional hyperbolic billiards
    • L. A. BUNIMOVICH, YA. G. SINAI and N. I. CHERNOV, Markov partitions for two-dimensional hyperbolic billiards, Russ. Math. Surv. 45 (1990), 105-152.
    • (1990) Russ. Math. Surv. , vol.45 , pp. 105-152
    • Bunimovich, L.A.1    Sinai, Ya.G.2    Chernov, N.I.3
  • 8
    • 84956084246 scopus 로고
    • Statistical properties of two-dimensional hyperbolic billiards
    • _, Statistical properties of two-dimensional hyperbolic billiards, Russ. Math. Surv. 46 (1991), 47-106.
    • (1991) Russ. Math. Surv. , vol.46 , pp. 47-106
  • 9
    • 21144471442 scopus 로고
    • Ergodic and statistical properties of piecewise linear hyperbolic automorphisms of the 2-torus
    • N. I. CHERNOV, Ergodic and statistical properties of piecewise linear hyperbolic automorphisms of the 2-torus, J. of Stat. Phys. 69 (1992), 111-134.
    • (1992) J. of Stat. Phys. , vol.69 , pp. 111-134
    • Chernov, N.I.1
  • 10
    • 21844520203 scopus 로고
    • Limit theorems and Markov approximations for chaotic dynamical systems
    • _, Limit theorems and Markov approximations for chaotic dynamical systems, Prob. Theory Related Fields 101 (1995), 321-362.
    • (1995) Prob. Theory Related Fields , vol.101 , pp. 321-362
  • 11
    • 6144222097 scopus 로고
    • Steady-state electrical conduction in the periodic Lorentz gas
    • [CELS] N. I. CHERNOV, G. EYINK, J. LEBOWITZ and YA G. SINAI, Steady-state electrical conduction in the periodic Lorentz gas, Comm. Math. Phys. 154 (1993), 569-601.
    • (1993) Comm. Math. Phys. , vol.154 , pp. 569-601
    • Chernov, N.I.1    Eyink, G.2    Lebowitz, J.3    Sinai, Ya.G.4
  • 12
    • 0002525106 scopus 로고
    • Positive Liapunov exponents and absolute continuity for maps of the interval
    • [CE] P. COLLET and J.-P. ECKMANN, Positive Liapunov exponents and absolute continuity for maps of the interval, Ergod. Th. & Dynam. Sys. 3 (1983), 13-46.
    • (1983) Ergod. Th. & Dynam. Sys. , vol.3 , pp. 13-46
    • Collet, P.1    Eckmann, J.-P.2
  • 13
    • 0001324823 scopus 로고
    • Ergodic properties of the Lozi mappings
    • P. COLLET and Y. LEVY, Ergodic properties of the Lozi mappings, Comm. Math. Phys. 93 (1984), 461-481.
    • (1984) Comm. Math. Phys. , vol.93 , pp. 461-481
    • Collet, P.1    Levy, Y.2
  • 15
    • 0000282259 scopus 로고
    • The central limit theorem for stationary processes
    • [G] M. I. GORDIN, The central limit theorem for stationary processes, Soviet Meth. Dokl. 10 (5) (1969), 1174-1176.
    • (1969) Soviet Meth. Dokl. , vol.10 , Issue.5 , pp. 1174-1176
    • Gordin, M.I.1
  • 16
    • 0000819591 scopus 로고
    • Ergodic properties of invariant measures for piecewise monotonic transformations
    • [HK] F. HOFBAUER and G. KELLER, Ergodic properties of invariant measures for piecewise monotonic transformations, Math. Z. 180 (1982), 119-140.
    • (1982) Math. Z. , vol.180 , pp. 119-140
    • Hofbauer, F.1    Keller, G.2
  • 18
    • 84974325915 scopus 로고
    • Nonexisterice of SBR measures for some diffeomorphisms that are "almost Anosov"
    • [HY] H. HU and L.-S. YOUNG, Nonexisterice of SBR measures for some diffeomorphisms that are "almost Anosov", Ergod. Th. & Dynam. Sys. 15 (1995), 67-76.
    • (1995) Ergod. Th. & Dynam. Sys. , vol.15 , pp. 67-76
    • Hu, H.1    Young, L.-S.2
  • 19
    • 0002053804 scopus 로고
    • Absolutely continuous invariant measures for one-parameter families of one-dimensional maps
    • [J] M. JAKOBSON, 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.1
  • 20
    • 0003280184 scopus 로고
    • Invariant manifolds, entropy and billiards; smooth maps with singularities
    • [KS] A. KATOK and J.-M. STRELCYN, Invariant Manifolds, Entropy and Billiards; Smooth Maps with Singularities, Springer Lecture Notes in Math. 1222 (1986).
    • (1986) Springer Lecture Notes in Math. , vol.1222
    • Katok, A.1    Strelcyn, J.-M.2
  • 21
    • 34250130646 scopus 로고
    • Central limit theorem for additive functionals of reversible Markov processes and applications to simple exclusions
    • [KV] C. KIPNIS and S.R.S. VARADHAN, Central limit theorem for additive functionals of reversible Markov processes and applications to simple exclusions, Comm. Math. Phys. 104 (1986), 1-19.
    • (1986) Comm. Math. Phys. , vol.104 , pp. 1-19
    • Kipnis, C.1    Varadhan, S.R.S.2
  • 22
    • 0007436260 scopus 로고
    • Un théorème de la limite centrale pour une classe de transformations monotones par morceaux
    • [Ke] G. KELLER, Un théorème de la limite centrale pour une classe de transformations monotones par morceaux, Comptes Rendus de l'Académie des Sciences, Série A 291 (1980), 155-158.
    • (1980) Comptes Rendus de l'Académie des Sciences, Série A , vol.291 , pp. 155-158
    • Keller, G.1
  • 23
    • 0002160620 scopus 로고
    • Special theory, zeta functions and the distribution of periodic points for Collet-Eckmann maps
    • [KN] G. KELLER and T. NOWICKI, Special theory, 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
  • 24
    • 84966227493 scopus 로고
    • On the existence of invariant measures for piecewise monotonic transformations
    • [LaY] A. LASOTA and J. YORKE, On the existence of invariant measures for piecewise monotonic transformations, Trans. A. M. S. 186 (1973), 481-488.
    • (1973) Trans. A. M. S. , vol.186 , pp. 481-488
    • Lasota, A.1    Yorke, J.2
  • 25
    • 51249183807 scopus 로고
    • Propriétés ergodiques des mesures de Sinai
    • [Le] F. LEDRAPPIER, Propriétés ergodiques des mesures de Sinai, Publ. Math. IHES 59 (1984), 163-188.
    • (1984) Publ. Math. IHES , vol.59 , pp. 163-188
    • Ledrappier, F.1
  • 26
    • 0000345142 scopus 로고
    • Decay of correlations
    • C. LIVERANI, Decay of correlations, Ann. of Math. 142 (1995), 239-301.
    • (1995) Ann. of Math. , vol.142 , pp. 239-301
    • Liverani, C.1
  • 27
    • 0002283776 scopus 로고    scopus 로고
    • Central limit theorem for deterministic systems
    • Eds. F. Ledrappier, J. Lewowicz, S. Newhouse, Pitman Research Notes in Math.
    • C. LIVERANI, Central limit theorem for deterministic systems, Int. Conf. of Dyn. Sys., Montevideo, 1995, Eds. F. Ledrappier, J. Lewowicz, S. Newhouse, Pitman Research Notes in Math. 362 (1996), 56-75.
    • (1996) Int. Conf. of Dyn. Sys., Montevideo, 1995 , vol.362 , pp. 56-75
    • Liverani, C.1
  • 28
    • 0242344635 scopus 로고
    • Abundance of strange attractors
    • L. MORA and M. VIANA, Abundance of strange attractors, Acta Math. 171 (1993), 1-71.
    • (1993) Acta Math. , vol.171 , pp. 1-71
    • Mora, L.1    Viana, M.2
  • 29
    • 0002046772 scopus 로고
    • Absolutely continuous invariant measures under a summability condition
    • [NS] T. NOWICKI and S. VAN STREIN, Absolutely continuous invariant measures under a summability condition. Invent. Math. 105 (1991), 123-136.
    • (1991) Invent. Math. , vol.105 , pp. 123-136
    • Nowicki, T.1    Van Strein, S.2
  • 30
    • 25544470047 scopus 로고
    • Zeta functions and the period orbit structure of hyperbolic dynamics
    • Paris
    • [PP] W. PARRY and M. POLLICOTT, Zeta Functions and the Period Orbit Structure of Hyperbolic Dynamics, Soc. Math, de France (Astérisque 187-188), Paris, 1990.
    • (1990) Soc. Math, de France Astérisque , vol.187-188
    • Parry, W.1    Pollicott, M.2
  • 31
    • 84961291543 scopus 로고
    • Characteristic Lyapunov exponents and smooth ergodic theory
    • YA. B. PESIN, Characteristic Lyapunov exponents and smooth ergodic theory, Russ. Math. Surveys 32 (1977), 55-114.
    • (1977) Russ. Math. Surveys , vol.32 , pp. 55-114
    • Pesin, Ya.B.1
  • 32
    • 84971972535 scopus 로고
    • Dynamical systems with generalized hyperbolic attractors: Hyperbolic, ergodic and topological properties
    • _, Dynamical systems with generalized hyperbolic attractors: hyperbolic, ergodic and topological properties, Ergod. Th. & Dynam. Sys. 12 (1992), 123-151.
    • (1992) Ergod. Th. & Dynam. Sys. , vol.12 , pp. 123-151
  • 33
    • 84966234619 scopus 로고
    • Ergodic attractors
    • [PS] C. PUGH and M. SHUB, Ergodic attractors, Trans. A. M. S. 312 (1989), 1-54.
    • (1989) Trans. A. M. S. , vol.312 , pp. 1-54
    • Pugh, C.1    Shub, M.2
  • 34
    • 0000809231 scopus 로고
    • A measure associated with Axiom-A attractors
    • D. RUELLE, 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
  • 35
    • 0004133384 scopus 로고
    • Addison-Wesley, New York
    • _, Thermodynamic Formalism, Addison-Wesley, New York, 1978.
    • (1978) Thermodynamic Formalism
  • 36
    • 0013554411 scopus 로고
    • Flots qui ne mélangent pas exponentiellement
    • _, Flots qui ne mélangent pas exponentiellement, C. R. Acad. Sci. Paris Sér. I Math. 296 (1983), 191-193.
    • (1983) C. R. Acad. Sci. Paris Sér. I Math. , vol.296 , pp. 191-193
  • 38
    • 84956071330 scopus 로고
    • Gibbs measures in ergodic theory
    • YA. G. SINAI, Gibbs measures in ergodic theory, Russ. Math. Surveys 27 (1972), 21-69.
    • (1972) Russ. Math. Surveys , vol.27 , pp. 21-69
    • Sinai, Ya.G.1
  • 39
    • 84927896522 scopus 로고
    • Dynamical systems with elastic reflections: Ergodic properties of dispers ing billiards
    • _, Dynamical systems with elastic reflections: Ergodic properties of dispers ing billiards. Russ. Math. Surveys 25 (1970), 137-189.
    • (1970) Russ. Math. Surveys , vol.25 , pp. 137-189
  • 40
    • 0005054205 scopus 로고
    • Positive Lyapunov exponent for generic one-parameter families of unimodal maps
    • Série I
    • P. THIEULLEN, C. TRESSER and L.-S. YOUNG, Positive Lyapunov exponent for generic one-parameter families of unimodal maps, C. R. Acad. Sci. Paris, t. 315 Série I (1992), 69-72; J'Analyse 64 (1994), 121-172.
    • (1992) C. R. Acad. Sci. Paris , vol.315 , pp. 69-72
    • Thieullen, P.1    Tresser, C.2    Young, L.-S.3
  • 41
    • 0001748121 scopus 로고
    • P. THIEULLEN, C. TRESSER and L.-S. YOUNG, Positive Lyapunov exponent for generic one-parameter families of unimodal maps, C. R. Acad. Sci. Paris, t. 315 Série I (1992), 69-72; J'Analyse 64 (1994), 121-172.
    • (1994) J'Analyse , vol.64 , pp. 121-172
  • 42
    • 0000176923 scopus 로고
    • Invariant families of cones and Lyapunov exponents
    • [W] M. WOJTKOWSKI, Invariant families of cones and Lyapunov exponents, Ergod. Th. & Dynam. Sys. 5 (1985), 145-161.
    • (1985) Ergod. Th. & Dynam. Sys. , vol.5 , pp. 145-161
    • Wojtkowski, M.1
  • 43
    • 84968486188 scopus 로고
    • A Bowen-Ruelle measure for certain piecewise hyperbolic maps
    • L.-S. YOUNG, A Bowen-Ruelle measure for certain piecewise hyperbolic maps, Trans. A. M. S. 287 (1985), 41-48.
    • (1985) Trans. A. M. S. , vol.287 , pp. 41-48
    • Young, L.-S.1
  • 44
    • 0001470078 scopus 로고
    • Decay of correlations for certain quadratic maps
    • _, Decay of correlations for certain quadratic maps, Comm. Math. Phys. 146 (1992), 123-138.
    • (1992) Comm. Math. Phys. , vol.146 , pp. 123-138


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.