메뉴 건너뛰기




Volumn 1, Issue PART A, 2002, Pages 409-452

Chapter 5 Periodic orbits and zeta functions

Author keywords

[No Author keywords available]

Indexed keywords


EID: 67649354433     PISSN: 1874575X     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S1874-575X(02)80007-8     Document Type: Article
Times cited : (10)

References (74)
  • 1
    • 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
  • 2
    • 2442681194 scopus 로고    scopus 로고
    • Topological methods in dynamics
    • Hasselblatt B., and Katok A. (Eds), Elsevier, Amsterdam
    • Franks J., and Misiurewicz M. Topological methods in dynamics. In: Hasselblatt B., and Katok A. (Eds). Handbook of Dynamical Systems Vol. 1A (2002), Elsevier, Amsterdam 547-598
    • (2002) Handbook of Dynamical Systems , vol.1 A , pp. 547-598
    • Franks, J.1    Misiurewicz, M.2
  • 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
    • 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. 1A (2002), Elsevier, Amsterdam 453-545
    • (2002) Handbook of Dynamical Systems , vol.1 A , pp. 453-545
    • Knieper, G.1
  • 5
    • 0033636318 scopus 로고    scopus 로고
    • Precise counting results for closed orbits of Anosov flows
    • Anantharaman N. Precise counting results for closed orbits of Anosov flows. Ann. Sci. École Norm. Sup. 33 (2000) 33-56
    • (2000) Ann. Sci. École Norm. Sup. , vol.33 , pp. 33-56
    • Anantharaman, N.1
  • 6
    • 0002869924 scopus 로고
    • On periodic points
    • Artin M., and Mazur B. On periodic points. Ann. of Math. 81 (1965) 82-99
    • (1965) Ann. of Math. , vol.81 , pp. 82-99
    • Artin, M.1    Mazur, B.2
  • 8
    • 0032377221 scopus 로고    scopus 로고
    • Periodic orbits and dynamical spectra
    • Baladi V. Periodic orbits and dynamical spectra. Ergodic Theory Dynamical Systems 18 (1998) 255-292
    • (1998) Ergodic Theory Dynamical Systems , vol.18 , pp. 255-292
    • Baladi, V.1
  • 9
    • 0001525001 scopus 로고
    • Zeta functions and transfer operators for piecewise monotone transformations
    • 459-177
    • 459-177. Baladi V., and Keller G. Zeta functions and transfer operators for piecewise monotone transformations. Comm. Math. Phys. 127 (1990)
    • (1990) Comm. Math. Phys. , vol.127
    • Baladi, V.1    Keller, G.2
  • 10
    • 0030543668 scopus 로고    scopus 로고
    • Sharp determinants
    • Baladi V., and Ruelle D. Sharp determinants. Invent. Math. 123 (1996) 553-574
    • (1996) Invent. Math. , vol.123 , pp. 553-574
    • Baladi, V.1    Ruelle, D.2
  • 11
    • 0002729084 scopus 로고
    • Periodic orbits for hyperbolic flows
    • Bowen R. Periodic orbits for hyperbolic flows. Amer. J. Math. 94 (1972) 1-30
    • (1972) Amer. J. Math. , vol.94 , pp. 1-30
    • Bowen, R.1
  • 12
    • 0000058449 scopus 로고
    • Symbolic dynamics for hyperbolic flows
    • Bowen R. Symbolic dynamics for hyperbolic flows. Amer. J. Math. 95 (1973) 429-460
    • (1973) Amer. J. Math. , vol.95 , pp. 429-460
    • Bowen, R.1
  • 13
    • 0003208028 scopus 로고
    • Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms
    • Springer, Berlin
    • Bowen R. Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms. Lecture Notes in Math. Vol. 470 (1975), Springer, Berlin
    • (1975) Lecture Notes in Math. , vol.470
    • Bowen, R.1
  • 14
    • 0002572491 scopus 로고
    • On Axiom a Diffeomorphisms
    • Amer. Math. Soc., Providence, RI
    • Bowen R. On Axiom a Diffeomorphisms. Regional Conf. Series Vol. 35 (1978), Amer. Math. Soc., Providence, RI
    • (1978) Regional Conf. Series , vol.35
    • Bowen, R.1
  • 15
    • 0003058997 scopus 로고
    • Zeta functions of restrictions of the shift transformation
    • Global Analysis. (Berkeley, CA, 1968)
    • Bowen R., and Lanford O. Zeta functions of restrictions of the shift transformation. Global Analysis. (Berkeley, CA, 1968). Proc. Sympos. Pure Math. 14 (1970) 43-49
    • (1970) Proc. Sympos. Pure Math. , vol.14 , pp. 43-49
    • Bowen, R.1    Lanford, O.2
  • 18
    • 33644538777 scopus 로고    scopus 로고
    • On the statistical properties of geodesic flows on negatively curved surfaces
    • Princeton University
    • Dolgopyat D. On the statistical properties of geodesic flows on negatively curved surfaces. Thesis (1997), Princeton University
    • (1997) Thesis
    • Dolgopyat, D.1
  • 19
    • 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 (1998) 357-390
    • (1998) Ann. of Math. , vol.147 , pp. 357-390
    • Dolgopyat, D.1
  • 20
    • 0032333778 scopus 로고    scopus 로고
    • Prevalence of fast mixing in hyperbolic flows
    • Dolgopyat D. Prevalence of fast mixing in hyperbolic flows. Ergodic Theory Dynamical Systems 5 (1998) 1097-1114
    • (1998) Ergodic Theory Dynamical Systems , vol.5 , pp. 1097-1114
    • Dolgopyat, D.1
  • 21
    • 22044444912 scopus 로고    scopus 로고
    • Addendum to: "Periodic orbits and dynamical spectra" by V. Baladi
    • Dolgopyat D., and Pollicott M. Addendum to: "Periodic orbits and dynamical spectra" by V. Baladi. Ergodic Theory Dynamical Systems 18 (1998) 293-301
    • (1998) Ergodic Theory Dynamical Systems , vol.18 , pp. 293-301
    • Dolgopyat, D.1    Pollicott, M.2
  • 23
    • 0001776020 scopus 로고
    • Homology and Dynamical Systems
    • Amer. Math. Soc., Providence, RI
    • Franks J. Homology and Dynamical Systems. Regional Conf. Series Vol. 49 (1982), Amer. Math. Soc., Providence, RI
    • (1982) Regional Conf. Series , vol.49
    • Franks, J.1
  • 24
    • 0002358477 scopus 로고
    • Flow equivalence of subshifts of finite type
    • Franks J. Flow equivalence of subshifts of finite type. Ergodic Theory Dynamical Systems 4 (1984) 53-66
    • (1984) Ergodic Theory Dynamical Systems , vol.4 , pp. 53-66
    • Franks, J.1
  • 25
    • 84968508599 scopus 로고
    • Period doubling and the Lefschetz formula
    • Franks J. Period doubling and the Lefschetz formula. Trans. Amer. Math. Soc. 287 (1985) 275-283
    • (1985) Trans. Amer. Math. Soc. , vol.287 , pp. 275-283
    • Franks, J.1
  • 26
    • 0000954685 scopus 로고
    • Generalizations of the Poincaré-Birkhoff theorem
    • Franks J. Generalizations of the Poincaré-Birkhoff theorem. Ann. of Math. 128 (1988) 139-151
    • (1988) Ann. of Math. , vol.128 , pp. 139-151
    • Franks, J.1
  • 27
    • 33751514484 scopus 로고
    • 2 and periodic points of annulus homeomorphisms
    • 2 and periodic points of annulus homeomorphisms. Invent. Math. 108 (1992) 402-418
    • (1992) Invent. Math. , vol.108 , pp. 402-418
    • Franks, J.1
  • 28
    • 0001407441 scopus 로고
    • The zeta functions of Ruelle and Selberg I
    • Fried D. The zeta functions of Ruelle and Selberg I. Ann. Sci. École Norm. Sup. 19 (1986) 491-517
    • (1986) Ann. Sci. École Norm. Sup. , vol.19 , pp. 491-517
    • Fried, D.1
  • 29
    • 0002703733 scopus 로고
    • Lefschetz formulas for flows
    • The Lefschetz Centennial Conference. (Mexico City, 1984), Amer. Math. Soc., Providence, RI
    • Fried D. Lefschetz formulas for flows. The Lefschetz Centennial Conference. (Mexico City, 1984). Contemp. Math. Vol. 58 III (1987), Amer. Math. Soc., Providence, RI 19-69
    • (1987) Contemp. Math. , vol.58 III , pp. 19-69
    • Fried, D.1
  • 30
    • 0038913623 scopus 로고
    • Rationality for isolated expansive sets
    • Fried D. Rationality for isolated expansive sets. Adv. in Math. 65 (1987) 35-38
    • (1987) Adv. in Math. , vol.65 , pp. 35-38
    • Fried, D.1
  • 31
    • 84976040758 scopus 로고
    • The flat-trace asymptotics of a uniform system of contractions
    • Fried D. The flat-trace asymptotics of a uniform system of contractions. Ergodic Theory Dynamical Systems 15 (1995) 1061-1071
    • (1995) Ergodic Theory Dynamical Systems , vol.15 , pp. 1061-1071
    • Fried, D.1
  • 34
    • 84971922644 scopus 로고
    • Meromorphic extension of the zeta function for Axiom A flows
    • Haydn N. Meromorphic extension of the zeta function for Axiom A flows. Ergodic Theory Dynamical Systems 10 (1990) 347-360
    • (1990) Ergodic Theory Dynamical Systems , vol.10 , pp. 347-360
    • Haydn, N.1
  • 35
    • 51249185076 scopus 로고
    • On intrinsic ergodicity of piecewise monotonic transformations with positive entropy
    • Hofbauer F. On intrinsic ergodicity of piecewise monotonic transformations with positive entropy. Israel J. Math. 34 (1979) 213-237
    • (1979) Israel J. Math. , vol.34 , pp. 213-237
    • Hofbauer, F.1
  • 36
    • 0002392544 scopus 로고
    • Zeta functions and transfer operators for piecewise linear transformations
    • Hofbauer F., and Keller G. Zeta functions and transfer operators for piecewise linear transformations. J. Reine Angew. Math. 352 (1984) 100-113
    • (1984) J. Reine Angew. Math. , vol.352 , pp. 100-113
    • Hofbauer, F.1    Keller, G.2
  • 37
    • 33645932436 scopus 로고
    • Zur analytischen Theorie hyperbolischen Raumformen und Bewegungsgruppen
    • Huber H. Zur analytischen Theorie hyperbolischen Raumformen und Bewegungsgruppen. Math. Ann. 138 (1959) 1-26
    • (1959) Math. Ann. , vol.138 , pp. 1-26
    • Huber, H.1
  • 38
    • 0001001304 scopus 로고
    • Homology and closed geodesies in a compact Riemann surface
    • Katsuda A., and Sunada T. Homology and closed geodesies in a compact Riemann surface. Amer. J. Math. 110 (1988) 145-155
    • (1988) Amer. J. Math. , vol.110 , pp. 145-155
    • Katsuda, A.1    Sunada, T.2
  • 39
    • 51249171872 scopus 로고
    • Closed orbits in homology classes
    • Katsuda A., and Sunada T. Closed orbits in homology classes. Publ. Math. 71 (1990) 5-32
    • (1990) Publ. Math. , vol.71 , pp. 5-32
    • Katsuda, A.1    Sunada, T.2
  • 40
    • 0002160620 scopus 로고
    • Spectral theory, zeta functions and the distribution of periodic orbits for Collet-Eckmann maps
    • Keller G., and Nowicki T. Spectral theory, zeta functions and the distribution of periodic orbits 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
  • 41
    • 0032623269 scopus 로고    scopus 로고
    • Fredholm determinants for hyperbolic diffeomorphisms of finite smoothness
    • Kitaev A. Fredholm determinants for hyperbolic diffeomorphisms of finite smoothness. Nonlinearity 12 (1999) 141-179
    • (1999) Nonlinearity , vol.12 , pp. 141-179
    • Kitaev, A.1
  • 42
    • 84972576554 scopus 로고
    • Closed geodesic in homology classes on surfaces of variable negative curvature
    • Lalley S. Closed geodesic in homology classes on surfaces of variable negative curvature. Duke Math.J. 58 (1989) 795-821
    • (1989) Duke Math.J. , vol.58 , pp. 795-821
    • Lalley, S.1
  • 43
    • 0002075858 scopus 로고
    • Über die Einteilung der positiven ganzen Zahlen in vier Klassen nach der Mindeszahl der zu ihrer additiven Zusammensetzung erforderlichen Quadrate
    • Landau E. Über die Einteilung der positiven ganzen Zahlen in vier Klassen nach der Mindeszahl der zu ihrer additiven Zusammensetzung erforderlichen Quadrate. Arch. Math. Phys. 13 (1908) 305-312
    • (1908) Arch. Math. Phys. , vol.13 , pp. 305-312
    • Landau, E.1
  • 44
    • 0000261098 scopus 로고
    • Lefschetz numbers for periodic points
    • Nielsen Theory and Dynamical Systems, Amer. Math. Soc., Providence, RI
    • Llibre J. Lefschetz numbers for periodic points. Nielsen Theory and Dynamical Systems. Contemp. Math. Vol. 152 (1993), Amer. Math. Soc., Providence, RI 215-227
    • (1993) Contemp. Math. , vol.152 , pp. 215-227
    • Llibre, J.1
  • 45
    • 0001570657 scopus 로고
    • Axiom A diffeomorphisms have rational zeta functions
    • Manning A. Axiom A diffeomorphisms have rational zeta functions. Bull. London Math. Soc. 3 (1971) 215-220
    • (1971) Bull. London Math. Soc. , vol.3 , pp. 215-220
    • Manning, A.1
  • 46
    • 0039476596 scopus 로고
    • Certain applications of ergodic theory to the investigation of manifolds of negative curvature
    • Margulis G. Certain applications of ergodic theory to the investigation of manifolds of negative curvature. Functional Anal. Appl. 3 (1969) 89-90
    • (1969) Functional Anal. Appl. , vol.3 , pp. 89-90
    • Margulis, G.1
  • 47
    • 0000848698 scopus 로고
    • On iterated maps of the interval, Dynamical Systems
    • Springer, Berlin
    • Milnor J., and Thurston W. On iterated maps of the interval, Dynamical Systems. Lecture Notes in Math. Vol. 1342 (1988), Springer, Berlin 465-563
    • (1988) Lecture Notes in Math. , vol.1342 , pp. 465-563
    • Milnor, J.1    Thurston, W.2
  • 48
    • 84958427130 scopus 로고
    • Bowen's equidistribution theory and the Dirichlet density theorem
    • Parry W. Bowen's equidistribution theory and the Dirichlet density theorem. Ergodic Theory Dynamical Systems 4 (1984) 117-134
    • (1984) Ergodic Theory Dynamical Systems , vol.4 , pp. 117-134
    • Parry, W.1
  • 49
    • 0000496951 scopus 로고
    • An analogue of the prime number theorem for closed orbits of Axiom A flows
    • Parry W., and Pollicott M. An analogue of the prime number theorem for closed orbits of Axiom A flows. Ann. of Math. 118 (1983) 573-591
    • (1983) Ann. of Math. , vol.118 , pp. 573-591
    • Parry, W.1    Pollicott, M.2
  • 50
    • 0000271607 scopus 로고
    • Zeta functions and the periodic orbit structure of hyperbolic dynamics
    • Parry W., and Pollicott M. Zeta functions and the periodic orbit structure of hyperbolic dynamics. Asterisque 187-188 (1990) 1-268
    • (1990) Asterisque , vol.187-188 , pp. 1-268
    • Parry, W.1    Pollicott, M.2
  • 51
    • 0000345033 scopus 로고
    • A topological invariant of flows on 1 -dimensional spaces
    • Parry W., and Sullivan D. A topological invariant of flows on 1 -dimensional spaces. Topology 14 (1975) 297-299
    • (1975) Topology , vol.14 , pp. 297-299
    • Parry, W.1    Sullivan, D.2
  • 52
    • 17044374336 scopus 로고
    • On the rate of mixing of Axiom A flows
    • Pollicott M. On the rate of mixing of Axiom A flows. Invent. Math. 81 (1985) 413-426
    • (1985) Invent. Math. , vol.81 , pp. 413-426
    • Pollicott, M.1
  • 53
    • 33646978879 scopus 로고
    • Meromorphic extensions of generalized zeta functions
    • Pollicott M. Meromorphic extensions of generalized zeta functions. Invent. Math. 85 (1986) 147-164
    • (1986) Invent. Math. , vol.85 , pp. 147-164
    • Pollicott, M.1
  • 54
    • 0000953395 scopus 로고
    • Homology and closed geodesics in a compact negatively curved surface
    • Pollicott M. Homology and closed geodesics in a compact negatively curved surface. Amer. J. Math. 113 (1991) 379-385
    • (1991) Amer. J. Math. , vol.113 , pp. 379-385
    • Pollicott, M.1
  • 55
    • 0037673876 scopus 로고
    • Orbit counting for some discrete groups acting on simply connected manifolds with negative curvature
    • Pollicott M., and Sharp R. Orbit counting for some discrete groups acting on simply connected manifolds with negative curvature. Invent. Math. 117 (1994) 275-302
    • (1994) Invent. Math. , vol.117 , pp. 275-302
    • Pollicott, M.1    Sharp, R.2
  • 56
    • 0000217012 scopus 로고    scopus 로고
    • Exponential error terms for growth functions on negatively curved surfaces
    • Pollicott M., and Sharp R. Exponential error terms for growth functions on negatively curved surfaces. Amer. J. Math. 120 (1998) 1019-1042
    • (1998) Amer. J. Math. , vol.120 , pp. 1019-1042
    • Pollicott, M.1    Sharp, R.2
  • 57
    • 67649349233 scopus 로고    scopus 로고
    • Asymptotic expansions for closed orbits in homology classes
    • to appear
    • M. Pollicott and R. Sharp, Asymptotic expansions for closed orbits in homology classes. Math. Ded., to appear.
    • Math. Ded
    • Pollicott, M.1    Sharp, R.2
  • 58
    • 51249187719 scopus 로고
    • Markov partitions for Anosov flows on n-dimensional manifolds
    • Ratner M. Markov partitions for Anosov flows on n-dimensional manifolds. Israel J. Math. 15 (1973) 92-114
    • (1973) Israel J. Math. , vol.15 , pp. 92-114
    • Ratner, M.1
  • 59
    • 84968469588 scopus 로고
    • Generalized zeta-functions for Axiom A basic sets
    • Ruelle D. Generalized zeta-functions for Axiom A basic sets. Bull. Amer. Math. Soc. 82 (1976) 153-156
    • (1976) Bull. Amer. Math. Soc. , vol.82 , pp. 153-156
    • Ruelle, D.1
  • 60
    • 0001085798 scopus 로고
    • Zeta-functions for expanding maps and Anosov flows
    • Ruelle D. Zeta-functions for expanding maps and Anosov flows. Invent. Math. 34 (1976) 231-242
    • (1976) Invent. Math. , vol.34 , pp. 231-242
    • Ruelle, D.1
  • 63
    • 51649157555 scopus 로고
    • An extension of the theory of Fredholm determinants
    • Ruelle D. An extension of the theory of Fredholm determinants. Publ. Math. (IHES) 72 (1990) 175-193
    • (1990) Publ. Math. (IHES) , vol.72 , pp. 175-193
    • Ruelle, D.1
  • 64
    • 67649368027 scopus 로고
    • Dynamical zeta functions: where do they come from and what are they good for?
    • (Leipzig, 1991), Springer, Berlin
    • (Leipzig, 1991). Ruelle D. Dynamical zeta functions: where do they come from and what are they good for?. Mathematical Physics Vol. X (1992), Springer, Berlin 43-51
    • (1992) Mathematical Physics , vol.X , pp. 43-51
    • Ruelle, D.1
  • 65
    • 0346149385 scopus 로고
    • Analytic completion for dynamical zeta functions
    • Ruelle D. Analytic completion for dynamical zeta functions. Helv. Phys. Acta 66 (1993) 181-191
    • (1993) Helv. Phys. Acta , vol.66 , pp. 181-191
    • Ruelle, D.1
  • 66
    • 0001147424 scopus 로고
    • The correlation spectrum for hyperbolic analytic maps
    • Rugh H. The correlation spectrum for hyperbolic analytic maps. Nonlinearity 5 (1992) 1237-1263
    • (1992) Nonlinearity , vol.5 , pp. 1237-1263
    • Rugh, H.1
  • 67
    • 0002072428 scopus 로고
    • Co-existence of cycles of a continuous mapping of the line into itself
    • Sharkovski A.N. Co-existence of cycles of a continuous mapping of the line into itself. Ukrain. Mat. 16 (1964)
    • (1964) Ukrain. Mat. , vol.16
    • Sharkovski, A.N.1
  • 68
    • 0002350116 scopus 로고
    • Harmonic analysis and discontinuous groups in weakly symmetric Riemannian spaces with applications to Dirichlet series
    • Selberg A. Harmonic analysis and discontinuous groups in weakly symmetric Riemannian spaces with applications to Dirichlet series. J. Indian Math. Soc. 20 (1956) 47-87
    • (1956) J. Indian Math. Soc. , vol.20 , pp. 47-87
    • Selberg, A.1
  • 70
    • 84956071330 scopus 로고
    • Gibbs measures in ergodic theory
    • Sinai Y. Gibbs measures in ergodic theory. Russian Math. Surveys 27 (1972) 21-69
    • (1972) Russian Math. Surveys , vol.27 , pp. 21-69
    • Sinai, Y.1
  • 71
    • 84968514104 scopus 로고
    • Differentiable dynamical systems
    • Smale S. Differentiable dynamical systems. Bull. Amer. Math. Soc. 73 (1967) 747-817
    • (1967) Bull. Amer. Math. Soc. , vol.73 , pp. 747-817
    • Smale, S.1
  • 74
    • 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 (1998) 585-650
    • (1998) Ann. of Math. , vol.147 , pp. 585-650
    • Young, L.-S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.