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A direct proof of the tail variational principle and its extension to maps

Published online by Cambridge University Press:  01 April 2009

DAVID BURGUET
DAVID BURGUET*
Affiliation:
CMLS - CNRS UMR 7640, École polytechnique, 91128 Palaiseau Cedex, France (email: [email protected])
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Abstract

Downarowicz [Entropy structure. J. Anal.96 (2005), 57–116] stated a variational principle for the tail entropy for invertible continuous dynamical systems of a compact metric space. We give here an elementary proof of this variational principle. Furthermore, we extend the result to the non-invertible case.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 29 , Issue 2 , April 2009 , pp. 357 - 369
Copyright
Copyright © Cambridge University Press 2008

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References

[1]Boyle, M. and Downarowicz, T.. The entropy theory of symbolic extension. Invent. Math. 156(1) (2004), 119–161.CrossRefGoogle Scholar
[2]Burguet, D.. Entropy in differentiable dynamical sytems. Thesis in preparation.Google Scholar
[3]Buzzi, J.. Intrinsic ergodicity for smooth interval maps. Israel J. Math. 100 (1997), 125–161.CrossRefGoogle Scholar
[4]Downarowicz, T.. Entropy structure. J. Anal. 96 (2005), 57–116.Google Scholar
[5]Downarowicz, T. and Serafin, J.. Fiber entropy and conditional variational principles in compact non-metrizable spaces. Fund. Math. 172 (2002), 217–247.CrossRefGoogle Scholar
[6]Katok, A.. Lyapounov exponents, entropy and periodic orbits for diffeomorphisms. Publ. Math. Inst. Hautes Études Sci. 51 (1980), 137–173.CrossRefGoogle Scholar
[7]Goodman, T. N. T.. Relating topological and measure entropy. Bull. London Math. Soc. 3 (1971), 176–180.CrossRefGoogle Scholar
[8]Goodwyn, L. W.. Topological entropy bounds measure-theoretic entropy. Proc. Amer. Math. Soc. 23(3) (1969), 679–688.CrossRefGoogle Scholar
[9]Ledrappier, F.. A Variational Principle for the Topological Conditional Entropy (Lecture Notes in Mathematics, 729). Springer, Berlin, 1979, pp. 78–88.Google Scholar
[10]Ledrappier, F. and Walters, P.. A relativised variational principle for continuous transformations. J. London Math. Soc. 16 (1977), 568–576.CrossRefGoogle Scholar
[11]Lindenstrauss, E.. Mean dimension, small entropy factors and an embedding theorem. Publ. Math. Inst. Hautes Études Sci. 89 (1999), 227–262.CrossRefGoogle Scholar
[12]Misiurewicz, M.. Diffeomorphism without any measure with maximal entropy. Bull. Acad. Pol. Sci. 10 (1973), 903–910.Google Scholar
[13]Misiurewicz, M.. A short proof of the variational principle for ℤd actions. Asterisque 40 (1976), 147–158.Google Scholar
[14]Misiurewicz, M.. Topological conditional entropy. Studia Math. 55 (1976), 175–200.CrossRefGoogle Scholar
[15]Newhouse, S.. Continuity properties of entropy. Ann. of Math. (2) 129 (1989), 215–235.CrossRefGoogle Scholar
[16]Walters, P.. An Introduction to Ergodic Theory. Springer, New York, 1982.CrossRefGoogle Scholar
[17]Yomdin, Y.. Volume growth and entropy. Israel J. Math. 57 (1987), 285–300.CrossRefGoogle Scholar