Lyapunov exponents, entropy and periodic orbits for diffeomorphisms
Publications Mathématiques de l'IHÉS, Tome 51 (1980), pp. 137-173.
@article{PMIHES_1980__51__137_0,
     author = {Katok, Anatole},
     title = {Lyapunov exponents, entropy and periodic orbits for diffeomorphisms},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {137--173},
     publisher = {Institut des Hautes \'Etudes Scientifiques},
     volume = {51},
     year = {1980},
     mrnumber = {573822},
     zbl = {0445.58015},
     language = {en},
     url = {http://www.numdam.org/item/PMIHES_1980__51__137_0/}
}
TY  - JOUR
AU  - Katok, Anatole
TI  - Lyapunov exponents, entropy and periodic orbits for diffeomorphisms
JO  - Publications Mathématiques de l'IHÉS
PY  - 1980
SP  - 137
EP  - 173
VL  - 51
PB  - Institut des Hautes Études Scientifiques
UR  - http://www.numdam.org/item/PMIHES_1980__51__137_0/
LA  - en
ID  - PMIHES_1980__51__137_0
ER  - 
%0 Journal Article
%A Katok, Anatole
%T Lyapunov exponents, entropy and periodic orbits for diffeomorphisms
%J Publications Mathématiques de l'IHÉS
%D 1980
%P 137-173
%V 51
%I Institut des Hautes Études Scientifiques
%U http://www.numdam.org/item/PMIHES_1980__51__137_0/
%G en
%F PMIHES_1980__51__137_0
Katok, Anatole. Lyapunov exponents, entropy and periodic orbits for diffeomorphisms. Publications Mathématiques de l'IHÉS, Tome 51 (1980), pp. 137-173. http://www.numdam.org/item/PMIHES_1980__51__137_0/

[1] R. Bowen, Topological entropy and Axiom A, Proc. Symp. Pure Math., A.M.S., Providence R.I., 14 (1970), 23-41. | MR | Zbl

[2] R. Bowen, Periodic points and measures for Axiom A diffeomorphisms, Trans. Amer. Math. Soc., 154 (1971). 377-397. | MR | Zbl

[3] R. Bowen, Periodic orbits for hyperbolic flows, Amer. J. Math., 94 (1972), 1-30. | MR | Zbl

[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. | Zbl

[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 | Zbl

[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 | Zbl

[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

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

[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

[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

[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

[13] V. I. Oseledec, Multiplicative ergodic theorem. Lyapunov characteristic numbers for dynamical systems, Trans. Moscow Math. Soc., 19 (1968), 197-221 ; translated from Russian. | MR | Zbl

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

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

[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

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

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

[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

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

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

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