Katok, Anatole
Lyapunov exponents, entropy and periodic orbits for diffeomorphisms
Publications Mathématiques de l'IHÉS, Tome 51 (1980) , p. 137-173
Zbl 0445.58015 | MR 81i:28022 | 11 citations dans Numdam
URL stable : http://www.numdam.org/item?id=PMIHES_1980__51__137_0

Bibliographie

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[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. MR 51 #14160 | Zbl 0598.58031

[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. MR 53 #3257 | Zbl 0299.54031

[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. Zbl 0383.58012

[9] Ja. B. Pesin, Characteristic Lyapunov exponents and smooth ergodic theory, Russian Math. Surveys, 32 (1977), 4, 55-114 ; translated from Russian. Zbl 0383.58011

[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. Zbl 0423.58013

[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. Zbl 0399.58010

[12] M. I. Brin, Ja. B. Pesin, Partially hyperbolic dynamical systems, Math. of the USSR-Izvestija, 8 (1974), 1, 177-218 ; translated from Russian. Zbl 0309.58017

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[14] M. Raghunathan, A proof of Oseledec's multiplicative ergodic theorem, Israel J. Math., to appear. Zbl 0415.28013

[15] M. I. Zaharevitch, Characteristic exponents and vector ergodic theorem (in Russian), Leningrad Univ. Vestnik, Math. Mech. Astr, 7-2, 1978, 28-34. Zbl 0414.28026

[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. Zbl 0448.58010

[17] D. Ruelle, An inequality for the entropy of differentiable maps, Bol. Soc. Bras. Mat., 9 (1978), 83-87. MR 80f:58026 | Zbl 0432.58013

[18] R. Bowen, Entropy for group automorphisms and homogenous spaces, Trans. Amer. Math. Soc., 153 (1971), 401-414. MR 43 #469 | Zbl 0212.29201

[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. Zbl 0248.58007

[20] S. Smale, Diffeomorphisms with many periodic points, Diff. and Comb. Topology, Princeton Univ. Press, Princeton, 1965, 63-80. MR 31 #6244 | Zbl 0142.41103

[21] D. Ruelle, Ergodic theory of differentiable dynamical systems, Publ. Math. I.H.E.S., 50 (1979), 27-58. Numdam | MR 81f:58031 | Zbl 0426.58014

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