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 (3)

• Equilibrium States for Random Non-uniformly Expanding Maps
• Equilibrium States for Non-uniformly expanding maps
• Some non-hyperbolic systems with strictly non-zero Lyapunov exponents for all invariant measures: Horseshoes with internal tangencies

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