Lyapunov exponents, entropy and periodic orbits for diffeomorphisms

Anatole Katok

Publications Mathématiques de l'IHÉS (1980)

  • Volume: 51, page 137-173
  • ISSN: 0073-8301

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Katok, 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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  1. [1] R. BOWEN, Topological entropy and Axiom A, Proc. Symp. Pure Math., A.M.S., Providence R.I., 14 (1970), 23-41. Zbl0207.54402MR41 #7066
  2. [2] R. BOWEN, Periodic points and measures for Axiom A diffeomorphisms, Trans. Amer. Math. Soc., 154 (1971). 377-397. Zbl0212.29103MR43 #8084
  3. [3] R. BOWEN, Periodic orbits for hyperbolic flows, Amer. J. Math., 94 (1972), 1-30. Zbl0254.58005MR45 #7749
  4. [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. [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. [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. [7] R. BOWEN, Some systems with unique equilibrium state, Math. Systems Theory, 8 (1975), 193-203. Zbl0299.54031MR53 #3257
  8. [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. [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. [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. [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. [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. [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. [14] M. RAGHUNATHAN, A proof of Oseledec's multiplicative ergodic theorem, Israel J. Math., to appear. Zbl0415.28013
  15. [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. [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. [17] D. RUELLE, An inequality for the entropy of differentiable maps, Bol. Soc. Bras. Mat., 9 (1978), 83-87. Zbl0432.58013MR80f:58026
  18. [18] R. BOWEN, Entropy for group automorphisms and homogenous spaces, Trans. Amer. Math. Soc., 153 (1971), 401-414. Zbl0212.29201MR43 #469
  19. [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. [20] S. SMALE, Diffeomorphisms with many periodic points, Diff. and Comb. Topology, Princeton Univ. Press, Princeton, 1965, 63-80. Zbl0142.41103MR31 #6244
  21. [21] D. RUELLE, Ergodic theory of differentiable dynamical systems, Publ. Math. I.H.E.S., 50 (1979), 27-58. Zbl0426.58014MR81f:58031
  22. [22] A. KATOK, Smooth Ergodic Theory, Lecture Notes, University of Maryland, in preparation. 

Citations in EuDML Documents

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  1. Anatole Katok, Jean-Paul Thouvenot, Slow entropy type invariants and smooth realization of commuting measure-preserving transformations
  2. Charles C. Pugh, The C 1 + α hypothesis in Pesin theory
  3. François Béguin, Sylvain Crovisier, Frédéric Le Roux, Construction of curious minimal uniquely ergodic homeomorphisms on manifolds : the Denjoy–Rees technique
  4. Sergiĭ Kolyada, Michał Misiurewicz, L’ubomír Snoha, Topological entropy of nonautonomous piecewise monotone dynamical systems on the interval
  5. A. Katok, A. Mezhirov, Entropy and growth of expanding periodic orbits for one-dimensional maps
  6. Étienne Ghys, Construction de champs de vecteurs sans orbite périodique
  7. Jérôme Buzzi, Ergodicité intrinsèque de produits fibrés d'applications chaotiques unidimensionnelles
  8. J. M. Gambaudo, S. Van Strien, C. Tresser, The periodic orbit structure of orientation preserving diffeomorphisms on D2 with topological entropy zero
  9. Meysam Nassiri, Enrique R. Pujals, Robust transitivity in hamiltonian dynamics
  10. Jérôme Buzzi, Puzzles of Quasi-Finite Type, Zeta Functions and Symbolic Dynamics for Multi-Dimensional Maps

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