On the approximation of dynamical indicators in systems with nonuniformly hyperbolic behavior
| Autor: | Fernando José Sánchez-Salas |
|---|---|
| Rok vydání: | 2015 |
| Předmět: |
Physics
Mathematics::Complex Variables General Mathematics 010102 general mathematics Dynamical Systems (math.DS) Riemannian manifold 01 natural sciences Measure (mathematics) Omega 010101 applied mathematics Topological pressure Combinatorics Positive entropy FOS: Mathematics Ergodic theory 37D25 37D35 Diffeomorphism Mathematics - Dynamical Systems 0101 mathematics Energy (signal processing) |
| DOI: | 10.48550/arxiv.1505.02473 |
| Popis: | 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 $P_{\mu}(\phi) = h(\mu) + \int\phi{d\mu}$. Then we introduce a class of potentials $\phi$ for which there exists sequence of basic sets $\Omega_n$ such that $P(f|\Omega_n,\phi) \to P(\phi)$. Comment: arXiv admin note: text overlap with arXiv:1303.5010 |
| Databáze: | OpenAIRE |
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