Lyapunov exponents, entropy and periodic orbits for diffeomorphisms
Publications Mathématiques de l'IHÉS (1980)
- Volume: 51, page 137-173
- ISSN: 0073-8301
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topKatok, Anatole. "Lyapunov exponents, entropy and periodic orbits for diffeomorphisms." Publications Mathématiques de l'IHÉS 51 (1980): 137-173. <http://eudml.org/doc/103967>.
@article{Katok1980,
author = {Katok, Anatole},
journal = {Publications Mathématiques de l'IHÉS},
keywords = {epsilon trajectories; invariant measures; periodic points; entropy; pseudo-orbit tracing; Lyapunov exponents; hyperbolic period points; transversal homoclinic point},
language = {eng},
pages = {137-173},
publisher = {Institut des Hautes Études Scientifiques},
title = {Lyapunov exponents, entropy and periodic orbits for diffeomorphisms},
url = {http://eudml.org/doc/103967},
volume = {51},
year = {1980},
}
TY - JOUR
AU - Katok, Anatole
TI - Lyapunov exponents, entropy and periodic orbits for diffeomorphisms
JO - Publications Mathématiques de l'IHÉS
PY - 1980
PB - Institut des Hautes Études Scientifiques
VL - 51
SP - 137
EP - 173
LA - eng
KW - epsilon trajectories; invariant measures; periodic points; entropy; pseudo-orbit tracing; Lyapunov exponents; hyperbolic period points; transversal homoclinic point
UR - http://eudml.org/doc/103967
ER -
References
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- [2] R. BOWEN, Periodic points and measures for Axiom A diffeomorphisms, Trans. Amer. Math. Soc., 154 (1971). 377-397. Zbl0212.29103MR43 #8084
- [3] R. BOWEN, Periodic orbits for hyperbolic flows, Amer. J. Math., 94 (1972), 1-30. Zbl0254.58005MR45 #7749
- [4] D. V. ANOSOV, On certain class of invariant sets of smooth dynamical systems (in Russian), Proc. 5th International Conf. on Non-linear Oscillations, vol. 2, Kiev, 1970, 39-45. Zbl0243.34085
- [5] A. B. KATOK, Dynamical systems with hyperbolic structure (in Russian), Ninth Summer Math. School, Kiev, published by Math. Inst. of the Ukrainian Acad. of Sci., 1972 ; revised edition Kiev, Naukova Dumka, 1976, 125-211 ; to be translated into English. Zbl0598.58031MR51 #14160
- [6] A. B. KATOK, Local properties of hyperbolic sets (in Russian). Addition to the Russian translation of Z. NITECKI, Differentiable Dynamics, Moscow, Mir, 1975, 214-232.
- [7] R. BOWEN, Some systems with unique equilibrium state, Math. Systems Theory, 8 (1975), 193-203. Zbl0299.54031MR53 #3257
- [8] Ja. B. PESIN, Families of invariant manifolds corresponding to non-zero characteristic exponents, Math. of the USSR-Izvestija, 10 (1976), 6, 1261-1305 ; translated from Russian. Zbl0383.58012
- [9] Ja. B. PESIN, Characteristic Lyapunov exponents and smooth ergodic theory, Russian Math. Surveys, 32 (1977), 4, 55-114 ; translated from Russian. Zbl0383.58011
- [10] Ja. B. PESIN, Description of π-partition of a diffeomorphism with invariant measure, Math. Notes of the USSR Acad. of Sci., 22 (1976), 1, 506-514 ; translated from Russian. Zbl0423.58013
- [11] Ja. B. PESIN, Geodesic flows on closed Riemannian surfaces without focal points, Math. of the USSR-Izvestija, 11 (1977), 6, 1195-1228 ; translated from Russian. Zbl0399.58010
- [12] M. I. BRIN, Ja. B. PESIN, Partially hyperbolic dynamical systems, Math. of the USSR-Izvestija, 8 (1974), 1, 177-218 ; translated from Russian. Zbl0309.58017
- [13] V. I. OSELEDEC, Multiplicative ergodic theorem. Lyapunov characteristic numbers for dynamical systems, Trans. Moscow Math. Soc., 19 (1968), 197-221 ; translated from Russian. Zbl0236.93034MR39 #1629
- [14] M. RAGHUNATHAN, A proof of Oseledec's multiplicative ergodic theorem, Israel J. Math., to appear. Zbl0415.28013
- [15] M. I. ZAHAREVITCH, Characteristic exponents and vector ergodic theorem (in Russian), Leningrad Univ. Vestnik, Math. Mech. Astr, 7-2, 1978, 28-34. Zbl0414.28026
- [16] S. KATOK, The estimation from above for the topological entropy of a diffeomorphism, Proc. Conf. on Dynamical Syst., Evanston, 1979, to appear in Lecture Notes in Math. Zbl0448.58010
- [17] D. RUELLE, An inequality for the entropy of differentiable maps, Bol. Soc. Bras. Mat., 9 (1978), 83-87. Zbl0432.58013MR80f:58026
- [18] R. BOWEN, Entropy for group automorphisms and homogenous spaces, Trans. Amer. Math. Soc., 153 (1971), 401-414. Zbl0212.29201MR43 #469
- [19] E. I. DINABURG, On the relations among various entropy characteristics of dynamical systems, Math. of the USSR-Izvestija, 5 (1971), 2, 337-378 ; translated from Russian. Zbl0248.58007
- [20] S. SMALE, Diffeomorphisms with many periodic points, Diff. and Comb. Topology, Princeton Univ. Press, Princeton, 1965, 63-80. Zbl0142.41103MR31 #6244
- [21] D. RUELLE, Ergodic theory of differentiable dynamical systems, Publ. Math. I.H.E.S., 50 (1979), 27-58. Zbl0426.58014MR81f:58031
- [22] A. KATOK, Smooth Ergodic Theory, Lecture Notes, University of Maryland, in preparation.
Citations in EuDML Documents
top- Anatole Katok, Jean-Paul Thouvenot, Slow entropy type invariants and smooth realization of commuting measure-preserving transformations
- Charles C. Pugh, The hypothesis in Pesin theory
- François Béguin, Sylvain Crovisier, Frédéric Le Roux, Construction of curious minimal uniquely ergodic homeomorphisms on manifolds : the Denjoy–Rees technique
- Sergiĭ Kolyada, Michał Misiurewicz, L’ubomír Snoha, Topological entropy of nonautonomous piecewise monotone dynamical systems on the interval
- A. Katok, A. Mezhirov, Entropy and growth of expanding periodic orbits for one-dimensional maps
- Étienne Ghys, Construction de champs de vecteurs sans orbite périodique
- Jérôme Buzzi, Ergodicité intrinsèque de produits fibrés d'applications chaotiques unidimensionnelles
- J. M. Gambaudo, S. Van Strien, C. Tresser, The periodic orbit structure of orientation preserving diffeomorphisms on D2 with topological entropy zero
- Meysam Nassiri, Enrique R. Pujals, Robust transitivity in hamiltonian dynamics
- Jérôme Buzzi, Puzzles of Quasi-Finite Type, Zeta Functions and Symbolic Dynamics for Multi-Dimensional Maps
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