Abstract
We derive several variational formulas for the topological entropy and SRB entropy of Axiom A flows on compact manifolds and for the Hausdorff dimension of basic sets for Axiom A diffeomorphisms on compact surfaces.
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References
R. Bowen,Equilibrium States and the Theory of Anosov Diffeomorphisms (Springer-Verlag).
G. Contreras, Regularity of topological and metric entropy of hyperbolic flows, preprint.
A. Katok, G. Knieper, and H. Weiss, Formulas for the derivative and critical points of topological entropy for Anosov and geodesic flows,Commun. Math. Phys. 138:19–31 (1991).
A. Katok, G. Knieper, M. Pollicott, and H. Weiss, Differentiability and analyticity of topological entropy for Anosov and geodesic flows,Invent. Math. 98:581–597 (1989).
G. Knieper and H. Weiss, Differentiability of measure theoretic entropy: I,Invent. Math. 95:579–589 (1989).
G. Knieper and H. Weiss, Smoothness of measure theoretic entropy for Anosov flows, Caltech Technical Report.
R. Mañé, The Hausdorff dimension of horseshoes diffeomorphisms of surfaces,Bol. Soc. Bras. Math. 20:1–24 (1990).
H. McCluskey and A. Manning, Hausdorff dimension for horseshoes,Ergodic Theory Dynam. Syst. 3:251–260 (1983).
D. Ruelle,Thermodynamic Formalism (Addison-Wesley, 1978).
P. Walters,An Introduction to Ergodic Theory (Springer-Verlag, 1982).
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Weiss, H. Some variational formulas for Hausdorff dimension, topological entropy, and SRB entropy for hyperbolic dynamical systems. J Stat Phys 69, 879–886 (1992). https://doi.org/10.1007/BF01050439
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DOI: https://doi.org/10.1007/BF01050439