Invariant manifolds and equilibrium states for non-uniformly hyperbolic horseshoes

Abstract

In this paper we consider horseshoes containing an orbit of homoclinic tangency accumulated by periodic points. We prove a version of the Invariant Manifolds Theorem, construct finite Markov partitions and use them to prove the existence and uniqueness of equilibrium states associated to Hölder continuous potentials.

33 pages, 6 figures

References in corpus (1)

• Some non-hyperbolic systems with strictly non-zero Lyapunov exponents for all invariant measures: Horseshoes with internal tangencies

Cited by in corpus (1)

• Existence, uniqueness and stability of equilibrium states for non-uniformly expanding maps