Lyapunov exponents, entropy and periodic orbits for diffeomorphisms

Anatole Katok

Publications Mathématiques de l'IHÉS (1980)

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

How to cite


Katok, Anatole. "Lyapunov exponents, entropy and periodic orbits for diffeomorphisms." Publications Mathématiques de l'IHÉS 51 (1980): 137-173. <>.

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 = {},
volume = {51},
year = {1980},

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 -
ER -


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  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. 
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  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
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  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
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  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
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  22. [22] A. KATOK, Smooth Ergodic Theory, Lecture Notes, University of Maryland, in preparation. 

Citations in EuDML Documents

  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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