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Pesin’s entropy formula for endomorphisms
Published online by Cambridge University Press: 22 January 2016
Abstract.
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In this paper we prove Pesin’s entropy formula for general C2 (or C1+α) (non-invertible) endomorphisms of a compact manifold preserving a smooth measure.
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- Copyright © Editorial Board of Nagoya Mathematical Journal 1998
References
[B]
Bahnmüller, J., Pesin’s entropy formula for expanding random dynamical systems, private communication.Google Scholar
[H]
Hu, Huyi, Pesin’s entropy formula for expanding maps, Adv. Math. Beijing, 19 (1990), 338–349.Google Scholar
[KSt]
A, Katok. and Strelcyn, J. M., Invariant Manifold, Entropy and Billiards; Smooth Maps with Singularities, Lec. Not. Math., 1222, Springer-Verlag, 1986.Google Scholar
[Le]
Ledrappier, F., Some properties of absolutely continuous invariant measures on an interval, Ergod. Th. Dynam. Sys., 1 (1981), 77.CrossRefGoogle Scholar
[LeSt]
Ledrappier, F. and Strelcyn, J. M., A proof of the estimation from below in Pesin’s entropy formula, Ergod. Th. Dynam. Sys., 2 (1982), 203–219.CrossRefGoogle Scholar
[LeY1]
Ledrappier, F. and Young, L.-S., The metric entropy of diffeomorphisms, Part I; Characterization of measures satisfying Pesin’s entropy formula, Part II: Relations between entropy, exponents and dimension, Ann. Math., 122 (1985), 509–574.Google Scholar
[LeY2]
Ledrappier, F. and Young, L.-S., Entropy formula for random transformations, Probab. Th. Rel. Fields, 80 (1988), 217–240.Google Scholar
[LiQ]
Liu, Pei-Dong and Qian, Min, Smooth Ergodic Theory of Random Dynamical Systems, Lec. Not. Math., 1606, Springer-Verlag, 1995.Google Scholar
[M1]
Mañé, R., A proof of Pesin’s formula, Ergod. Th. Dynam. Sys., 1 (1981), 95–102.CrossRefGoogle Scholar
[M2]
Mañé, R., Ergodic Theory and Differentiable Dynamics, Springer-Verlag, 1987.CrossRefGoogle Scholar
[Pa]
Parry, W., Entropy and Generators in Ergodic Theory, W. A. Benjamin, Inc., New York, 1969.Google Scholar
[Pe]
Pesin, Ya. B., Lyapunov characteristic exponents and smooth ergodic theory, Russ. Math. Surveys, 32: 4 (1977), 55–114.Google Scholar
[QZ]
Qian, Min and Zhang, Zhu-Sheng, Ergodic theory of Axiom A endomorphisms, Ergod. Th. Dynam. Sys., 1 (1995), 161–174.Google Scholar
[R1]
Ruelle, D., An inequality for the entropy of differentiable maps, Bol. Soc. Bras. Math., 9 (1978), 83–87.Google Scholar
[R2]
Ruelle, D., Characteristic exponents and invariant manifolds in Hilbert space, Ann. Math., 115 (1982), 243–290.Google Scholar
[RSh]
Ruelle, D. and Shub, M., Stable manifolds for maps, Lec. Not. Math., 819, Springer-Verlag, 1980, pp. 389–392.Google Scholar
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