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arXiv · 1505.02473

On the approximation of dynamical indicators in systems with nonuniformly hyperbolic behavior

Fernando José Sánchez-Salas
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Abstract

Let $f$ be a $C^{1+α}$ diffeomorphism of a compact Riemannian manifold and $μ$ an ergodic hyperbolic measure with positive entropy. We prove that for every continuous potential $ϕ$ there exists a sequence of basic sets $Ω_n$ such that the topological pressure $P(f|Ω_n,ϕ)$ converges to the free energy $P_μ(ϕ) = h(μ) + \intϕ{dμ}$. Then we introduce a class of potentials $ϕ$ for which there exists sequence of basic sets $Ω_n$ such that $P(f|Ω_n,ϕ) \to P(ϕ)$.

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Fernando José Sánchez-Salas. 2015-10-20. On the approximation of dynamical indicators in systems with nonuniformly hyperbolic behavior. https://arxiv.org/abs/1505.02473

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