On the approximation of dynamical indicators in systems with nonuniformly hyperbolic behavior |
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Authors: | Email author" target="_blank">Fernando?José?Sánchez-SalasEmail author |
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Institution: | 1.Departamento de Matemáticas, Facultad Experimental de Ciencias,Universidad del Zulia,Maracaibo,Venezuela |
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Abstract: | Let f be a \(C^{1+\alpha }\) diffeomorphism of a compact Riemannian manifold and \(\mu \) an ergodic hyperbolic measure with positive entropy. We prove that for every continuous potential \(\phi \) there exists a sequence of basic sets \(\Omega _n\) such that the topological pressure \(P(f|\Omega _n,\phi )\) converges to the free energy \(P_{\mu }(\phi ) = h(\mu ) + \int \phi {d\mu }\). We also prove that for a suitable class of potentials \(\phi \) there exists a sequence of basic sets \(\Omega _n\) such that \(P(f|\Omega _n,\phi ) \rightarrow P(\phi )\). |
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