Equilibrium states of almost Anosov diffeomorphisms

Dominic Veconi

doi:10.3934/dcds.2020061

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2020, Volume 40, Issue 2: 767-780. Doi: 10.3934/dcds.2020061

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Equilibrium states of almost Anosov diffeomorphisms

Dominic Veconi

Department of Mathematics, Pennsylvania State University, University Park, PA 16802, USA

Received: December 31, 2018

Revised: July 31, 2019

Published: November 2019

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Abstract

We develop a thermodynamic formalism for a class of diffeomorphisms of a torus that are "almost-Anosov". In particular, we use a Young tower construction to prove the existence and uniqueness of equilibrium states for a collection of non-Hölder continuous geometric potentials over almost Anosov systems with an indifferent fixed point, as well as prove exponential decay of correlations and the central limit theorem for these equilibrium measures.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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References

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