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Ergodic theory of differentiable dynamical systems. (English) Zbl 0426.58014


MSC:

37C75 Stability theory for smooth dynamical systems
37A99 Ergodic theory
60F15 Strong limit theorems

References:

[1] M. A. Akcoglu andL. Sucheston,A ratio ergodic theorem for superadditive processes, to appear.
[2] R. Bowen andD. Ruelle, The ergodic theory of Axiom A flows,Inventiones math.,29 (1975), 181–202. · Zbl 0311.58010 · doi:10.1007/BF01389848
[3] Y. Derriennic, Sur le théorème ergodique sous-additif,C.R.A.S. Paris,281 A (1975), 985–988. · Zbl 0327.60028
[4] H. Furstenberg andH. Kesten, Products of random matrices,Ann. Math. Statist.,31 (1960), 457–469. · Zbl 0137.35501 · doi:10.1214/aoms/1177705909
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[7] K. Jacobs,Lecture notes on ergodic theory (2 vol.), Aarhus, Aarhus Universitet, 1963. · Zbl 0196.31301
[8] S. Katok,The estimation from above for the topological entropy of a diffeomorphism, to appear. · Zbl 0448.58010
[9] J. F. C. Kingman, The ergodic theory of subadditive stochastic processes,J. Royal Statist. Soc.,B 30 (1968), 499–510. · Zbl 0182.22802
[10] J. F. C. Kingman,Subadditive processes, in École d’été des probabilités de Saint-Flour, Lecture Notes in Math., no 539, Berlin, Springer, 1976.
[11] V. I. Oseledec, A multiplicative ergodic theorem. Ljapunov characteristic numbers for dynamical systems,Trudy Moskov. Mat. Obšč.,19 (1968), 179–210. English transl.Trans. Moscow Math Soc.,19 (1968), 197–231.
[12] Ya. B. Pesin, Lyapunov characteristic exponents and ergodic properties of smooth dynamical systems with an invariant measure,Dokl. Akad. Nauk SSSR,226, no 4 (1976), 774–777. English transl.Soviet Math. Dokl.,17, no 1 (1976), 196–199.
[13] Ya. B. Pesin, Invariant manifold families which correspond to nonvanishing characteristic exponents,Izv. Akad. Nauk SSSR, Ser. Mat.40, no 6 (1976), 1332–1379. English transl.Math. USSR Izvestija,10, no 6 (1976), 1261–1305.
[14] Ya. B. Pesin, Lyapunov characteristic exponents and smooth ergodic theory,Uspehi Mat. Nauk,32, no 4 (196) (1977), 55–112. English transl.,Russian Math. Surveys,32, no 4 (1977), 55–114. · Zbl 0383.58011
[15] M. S. Raghunathan, A proof of Oseledec’ multiplicative ergodic theorem.Israel. J. Math., to appear. · Zbl 0415.28013
[16] D. Ruelle, A measure associated with axiom A attractors,Amer. J. Math.,98 (1976), 619–654. · Zbl 0355.58010 · doi:10.2307/2373810
[17] D. Ruelle, An inequality for the entropy of differentiable maps,Bol. Soc. Bras. Mat.,9 (1978), 83–87. · Zbl 0432.58013 · doi:10.1007/BF02584795
[18] D. Ruelle, Sensitive dependence on initial condition and turbulent behavior of dynamical systems,Ann. N.Y. Acad. Sci., to appear. · Zbl 0438.58003
[19] Ya. G. Sinai, Gibbs measures in ergodic theory,Uspehi Mat. Nauk,27, no 4 (1972), 21–64. English transl.Russian Math. Surveys,27, no 4 (1972), 21–69. · Zbl 0246.28008
[20] S. Smale, Notes on differentiable dynamical systems,Proc. Sympos. Pure Math.,14, A.M.S., Providence, R. I. (1970), pp. 277–287. · Zbl 0205.54201
[21] J. Tits, Travaux de Margulis sur les sous-groupes discrets de groupes de Lie,Séminaire Bourbaki, exposé no 482 (1976), Lecture Notes in Math., no 567, Berlin, Springer, 1977.
[22] A. Weil,Basic number theory, Berlin, Springer, 1973, 2nd ed. · Zbl 0267.12001
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