Invariant manifolds and equilibrium states for non-uniformly hyperbolic horseshoes
نویسندگان
چکیده
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.
منابع مشابه
Some Non-hyperbolic Systems with Strictly Non-zero Lyapunov Exponents for All Invariant Measures: Horseshoes with Internal Tangencies
We study the hyperbolicity of a class of horseshoes exhibiting an internal tangency, i.e. a point of homoclinic tangency accumulated by periodic points. In particular these systems are strictly not uniformly hyperbolic. However we show that all the Lyapunov exponents of all invariant measures are uniformly bounded away from 0. This is the first known example of this kind.
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تاریخ انتشار 2008