English

A note on Eckmann-Ruelle's conjecture

Dynamical Systems 2015-08-07 v1

Abstract

We introduce a class of C1+αC^{1+\alpha} isolated nonuniformly hyperbolic sets Λ\Lambda for which supμMf{h(μ)χ+(μ)}\sup_{\mu \in {\mathcal M}_f}\{h(\mu) - \chi^+(\mu)\} equals the rate of escape from Λ\Lambda, where χ+(μ)\chi^+(\mu) is the average of the sum of positive Lyapunov exponents counted with their multiplicity.

Cite

@article{arxiv.1508.01313,
  title  = {A note on Eckmann-Ruelle's conjecture},
  author = {Fernando José Sánchez-Salas},
  journal= {arXiv preprint arXiv:1508.01313},
  year   = {2015}
}
R2 v1 2026-06-22T10:27:38.698Z