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arXiv · 1508.01313

A note on Eckmann-Ruelle's conjecture

Fernando José Sánchez-Salas
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Abstract

We introduce a class of $C^{1+\alpha}$ isolated nonuniformly hyperbolic sets $\Lambda$ for which $\sup_{\mu \in {\mathcal M}_f}\{h(\mu) - \chi^+(\mu)\}$ equals the rate of escape from $\Lambda$, where $\chi^+(\mu)$ is the average of the sum of positive Lyapunov exponents counted with their multiplicity.

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Fernando José Sánchez-Salas. 2015-08-06. A note on Eckmann-Ruelle's conjecture. https://arxiv.org/abs/1508.01313

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