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arXiv · 1303.5010

Variational principles and approximation of dynamical indicators for systems with nonuniformly hyperbolic behavior

Fernando José Sánchez-Salas
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Abstract

This note is concerned with approximation of dynamical indicators as pressures, Lyapunov exponents and dimension-like quantities, in systems with nonuniformly hyperbolic behavior. For this we let $P^*(\Phi) := \sup_{\mu}\{h(\mu) + \mu(\Phi)\}$ be a variational pressure defined over a suitable class of Borel measurable potentials and prove that, for regular nonuniformly hyperbolic systems, $P^*(\Phi) = \sup_{\Omega}P^*(f|\Omega,\Phi)$, supremum taken over the family of $f$-invariant uniformly hyperbolic basic sets. We then apply this variational principle to the approximation of dynamical indicators by horseshoes.

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Fernando José Sánchez-Salas. 2013-03-20. Variational principles and approximation of dynamical indicators for systems with nonuniformly hyperbolic behavior. https://arxiv.org/abs/1303.5010

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