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Volumn 348, Issue 8, 1996, Pages 2999-3013

Topological entropy of standard type monotone twist maps

Author keywords

Ergodic theory; Hyperbolic sets; Invariant measures; Lyapunov exponents; Monotone twist maps; Topological entropy; Variational principles

Indexed keywords


EID: 21344454623     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9947-96-01728-x     Document Type: Article
Times cited : (10)

References (32)
  • 1
    • 84972102711 scopus 로고
    • Monotone recurrence relations, their Birkhoff orbits and topological entropy
    • MR 91b:58181
    • [Ang 90] S. Angenent. Monotone recurrence relations, their Birkhoff orbits and topological entropy. Erg. Th. Dyn. Sys., 10:15-41, 1990. MR 91b:58181
    • (1990) Erg. Th. Dyn. Sys. , vol.10 , pp. 15-41
    • Angenent, S.1
  • 2
    • 0039641251 scopus 로고
    • A remark on the topological entropy and invariant circles of an area preserving twist map
    • Eds. R. Mc Gehee, K. Meyer, Springer, MR 94d:58078
    • [Ang 92] S. Angenent. A remark on the topological entropy and invariant circles of an area preserving twist map. In "Twist Mappings and Their Applications", IMA Volumes in Mathematics, Vol. 44., Eds. R. Mc Gehee, K. Meyer, Springer, 1992, pp. 1-5. MR 94d:58078
    • (1992) "Twist Mappings and Their Applications", IMA Volumes in Mathematics , vol.44 , pp. 1-5
    • Angenent, S.1
  • 3
    • 0000148713 scopus 로고
    • Chaotic trajectories in the standard map. the concept of anti-integrability
    • MR 91j:58100
    • [Aub 90] S. Aubry, G. Abramovici. Chaotic trajectories in the standard map. The concept of anti-integrability. Physica D, 43:199-219, 1990. MR 91j:58100
    • (1990) Physica D , vol.43 , pp. 199-219
    • Aubry, S.1    Abramovici, G.2
  • 4
    • 0002544793 scopus 로고
    • The concept of anti-integrability: Definition, theorems and applications to the standard map
    • Eds. R. Mc Gehee, K. Meyer, Springer, MR 94c:58179
    • [Aub 92a] S. Aubry. The concept of anti-integrability: definition, theorems and applications to the standard map. In "Twist Mappings and Their Applications", IMA Volumes in Mathematics, Vol. 44., Eds. R. Mc Gehee, K. Meyer, Springer, 1992, pp. 7-54. MR 94c:58179
    • (1992) Twist Mappings and Their Applications", IMA Volumes in Mathematics , vol.44 , pp. 7-54
    • Aubry, S.1
  • 5
    • 0002946916 scopus 로고
    • Equivalence of uniform hyperbolicity for symplectic twist maps and phonon gap for Frenkel-Kontorova models
    • MR 93e:58144
    • [Aub 92b] S. Aubry, R. S. Mackay, C. Baesens C. Equivalence of uniform hyperbolicity for symplectic twist maps and phonon gap for Frenkel-Kontorova models. Physica D, 56:123-134, 1992. MR 93e:58144
    • (1992) Physica D , vol.56 , pp. 123-134
    • Aubry, S.1    Mackay, R.S.2    Baesens, C.3
  • 6
    • 0000200057 scopus 로고
    • Anti-integrability in dynamical and variational problems
    • CMP 1996:2. Added in Proof
    • [Aub 95] S. Aubry. Anti-integrability in dynamical and variational problems, Physica D 86: 284-296, 1995. CMP 1996:2. [Added in Proof]
    • (1995) Physica D , vol.86 , pp. 284-296
    • Aubry, S.1
  • 7
    • 0001824105 scopus 로고
    • Mather sets for twist maps and geodesics on tori
    • MR 90a:58145
    • [Ban 88] V. Bangert. Mather sets for twist maps and geodesics on tori. Dynamics Reported, 1:1-55, 1988. MR 90a:58145
    • (1988) Dynamics Reported , vol.1 , pp. 1-55
    • Bangert, V.1
  • 8
    • 0013501719 scopus 로고
    • The ergodic theory of axiom A flows
    • MR 52:1786
    • [Bow 75] R. Bowen, D. Ruelle. The ergodic theory of axiom A flows. Inventiones Math., 29:181-202, 1975. MR 52:1786
    • (1975) Inventiones Math. , vol.29 , pp. 181-202
    • Bowen, R.1    Ruelle, D.2
  • 9
    • 0002734536 scopus 로고
    • Proof of the Poincaré-Birkhoff fixed point theorem
    • MR 56:6646
    • [Bro 75] M. Brown, W. D. Neumann. Proof of the Poincaré-Birkhoff fixed point theorem. Michigan Math. 3., 24:21-31, 1975. MR 56:6646
    • (1975) Michigan Math. 3. , vol.24 , pp. 21-31
    • Brown, M.1    Neumann, W.D.2
  • 12
    • 85012297095 scopus 로고
    • Plenty of elliptic islands for the standard family of area preserving maps
    • MR 95k:58115. [Added in Proof]
    • [Dua 94] P. Duarte. Plenty of elliptic islands for the standard family of area preserving maps, Ann. Inst. H. Poincaré Anal. Non Linéaire 11:359-409, 1994. MR 95k:58115. [Added in Proof]
    • (1994) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.11 , pp. 359-409
    • Duarte, P.1
  • 13
    • 0009970427 scopus 로고
    • Expansiveness, hyperbolicity and Hausdorff dimension
    • MR 90m:58159
    • [Fat 89] A. Fathi. Expansiveness, hyperbolicity and Hausdorff dimension. Commun. Math. Phys., 126: 249-262, 1989. MR 90m:58159
    • (1989) Commun. Math. Phys. , vol.126 , pp. 249-262
    • Fathi, A.1
  • 14
    • 38249016433 scopus 로고
    • Transversal homoclinic points of a class of conservative diffeomorphisms
    • MR 91j:58095
    • [Fon 90] E. Fontich. Transversal homoclinic points of a class of conservative diffeomorphisms. J. Diff. Equ., 5, 87:1-27, 1990. MR 91j:58095
    • (1990) J. Diff. Equ. , vol.5 , Issue.87 , pp. 1-27
    • Fontich, E.1
  • 15
    • 84974281116 scopus 로고
    • Dynamical properties of plane polynomial automorphisms
    • MR 90f:58163
    • [Fri 89] S. Friedland, J. Milnor. Dynamical properties of plane polynomial automorphisms. Ergod. Th. & Dynam. Sys. 9:67-99, 1989. MR 90f:58163
    • (1989) Ergod. Th. & Dynam. Sys. , vol.9 , pp. 67-99
    • Friedland, S.1    Milnor, J.2
  • 16
    • 0000652097 scopus 로고
    • Sur les courbes invariantes par les difféomorphismes de l'anneau
    • Société Mathématique de France, MR 85m:58062
    • [Her 83] M. Herman. Sur les courbes invariantes par les difféomorphismes de l'anneau. Astérisque, 103-104, Société Mathématique de France, 1983. MR 85m:58062
    • (1983) Astérisque , pp. 103-104
    • Herman, M.1
  • 17
    • 24544432762 scopus 로고
    • Iteration of the coupled map lattice construction
    • [Jak 95] A. Jakobsen and O. Knill. Iteration of the coupled map lattice construction, Phys. Lett. A 205:179-183, 1995.
    • (1995) Phys. Lett. A , vol.205 , pp. 179-183
    • Jakobsen, A.1    Knill, O.2
  • 18
    • 33645950994 scopus 로고    scopus 로고
    • Added in Proof
    • CMP 1996:1. [Added in Proof]
    • (1996) , vol.1
  • 19
    • 51649161951 scopus 로고
    • Lyapunov exponents, entropy, and periodic orbits for diffeomorphisms
    • MR 81i:28022
    • [Kat 80] A. Katok. Lyapunov exponents, entropy, and periodic orbits for diffeomorphisms. Publ.Math. IHES, 51:137-172, 1980. MR 81i:28022
    • (1980) Publ.Math. IHES , vol.51 , pp. 137-172
    • Katok, A.1
  • 20
    • 84958441479 scopus 로고
    • Some remarks on Birkhoff and Mather twist map theorems
    • MR 84m:58041
    • [Kat 82] A. Katok. Some remarks on Birkhoff and Mather twist map theorems. Ergod. Th. & Dynam. Sys., 2:185-194, 1982. MR 84m:58041
    • (1982) Ergod. Th. & Dynam. Sys. , vol.2 , pp. 185-194
    • Katok, A.1
  • 21
    • 21144461854 scopus 로고
    • Isospectral deformations of random Jacobi operators
    • MR 94J-.58136
    • [Kni 93] O. Knill. Isospectral deformations of random Jacobi operators. Commun. Math. Phys., 151:403-426, 1993. MR 94J-.58136
    • (1993) Commun. Math. Phys. , vol.151 , pp. 403-426
    • Knill, O.1
  • 22
    • 0009276293 scopus 로고
    • Isospectral deformation of discrete random Laplacians
    • Ed.: M.Fannes et al., Plenum Press, New York
    • [Kni 94] O. Knill. Isospectral deformation of discrete random Laplacians. In "On Three Levels", Ed.: M.Fannes et al., Plenum Press, New York, 1994, pp. 312-330.
    • (1994) On Three Levels , pp. 312-330
    • Knill, O.1
  • 23
    • 0039034738 scopus 로고
    • Percival variational principle for invariant measures and commensurate-incommensurate phase transitions in one dimensional chains
    • MR 86k:58072
    • [Laz 84] V. F. Lazutkin, D. Ya. Terman. Percival variational principle for invariant measures and commensurate-incommensurate phase transitions in one dimensional chains. Commun. Math. Phys, 94:511-522, 1984. MR 86k:58072
    • (1984) Commun. Math. Phys , vol.94 , pp. 511-522
    • Lazutkin, V.F.1    Terman, D.Ya.2
  • 24
    • 0003335289 scopus 로고
    • Ergodic Theory and differentiable Dynamics
    • New York, Springer, MR 88c:58040
    • [Man 87] R. Mané. Ergodic Theory and differentiable Dynamics. Ergebnisse der Mathematik und ihrer Grenzgebiete; Ser. 3, Bd. 8, New York, Springer, 1987. MR 88c:58040
    • (1987) Ergebnisse der Mathematik und ihrer Grenzgebiete; Ser. 3 , vol.8
    • Mané, R.1
  • 25
    • 0000456667 scopus 로고
    • Existence of quasi-periodic orbits for twist homeomorphism of the annulus
    • MR 84g:58084
    • [Mat 82] J. Mather. Existence of quasi-periodic orbits for twist homeomorphism of the annulus. Topology, 21:457-467, 1982. MR 84g:58084
    • (1982) Topology , vol.21 , pp. 457-467
    • Mather, J.1
  • 26
    • 0038246022 scopus 로고
    • Amount of rotation about a point and the Morse index
    • MR 86c:58051
    • [Mat 84] J. Mather. Amount of rotation about a point and the Morse index. Comm. Math. Phys., 94:141-153, 1984. MR 86c:58051
    • (1984) Comm. Math. Phys. , vol.94 , pp. 141-153
    • Mather, J.1
  • 28
    • 0001685281 scopus 로고
    • Continuity properties of entropy
    • MR 90f:58108; 90m:58117
    • [New 89] S. Newhouse. Continuity properties of entropy. Annals of Mathematics, 129:215-235, 1989. MR 90f:58108; 90m:58117
    • (1989) Annals of Mathematics , vol.129 , pp. 215-235
    • Newhouse, S.1
  • 29
    • 0011400243 scopus 로고
    • Factors of Bernoulli shifts are Bernoulli shifts
    • MR 43:478b
    • [Orn 70] D. S. Ornstein. Factors of Bernoulli shifts are Bernoulli shifts. Adv. Math., 5:349-364, 1970. MR 43:478b
    • (1970) Adv. Math. , vol.5 , pp. 349-364
    • Ornstein, D.S.1
  • 30
    • 0000928930 scopus 로고
    • Variational principle for invariant tori and cantori
    • MR 82m:58040
    • [Per 80] I. C. Percival. Variational principle for invariant tori and cantori. Amer. Instit. of Physics Conf. Proc., 57:310-320, 1980. MR 82m:58040
    • (1980) Amer. Instit. of Physics Conf. Proc. , vol.57 , pp. 310-320
    • Percival, I.C.1
  • 31
    • 0003348167 scopus 로고
    • Ergodic Theory
    • Cambridge University Press, Cambridge, MR 87i:28002
    • [Pet 83] K. Petersen. Ergodic Theory. Cambridge Studies in Advanced Mathematics 2. Cambridge University Press, Cambridge, 1983. MR 87i:28002
    • (1983) Cambridge Studies in Advanced Mathematics , vol.2
    • Petersen, K.1
  • 32
    • 84968491239 scopus 로고
    • On the prevalence of horseshoes
    • MR 82g:58070
    • [You 81] L-S. Young. On the prevalence of horseshoes. Trans. Amer. Math. Soc., 263:75-88, 1981. MR 82g:58070
    • (1981) Trans. Amer. Math. Soc. , vol.263 , pp. 75-88
    • Young, L.-S.1


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