Invariant manifolds and equilibrium states for non-uniformly hyperbolic horseshoes

Mathematics – Dynamical Systems

Scientific paper

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33 pages, 6 figures

Scientific paper

10.1088/0951-7715/19/11/009

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 H\"older
continuous potentials.

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