Equilibrium states for maps isotopic to Anosov

Abstract

In this work we address the problem of existence and uniqueness (finiteness) of ergodic equilibrium states for partially hyperbolic diffeomorphisms isotopic to Anosov on ${\mathbb{T}}^4$, with 2-dimensional center foliation. To do so we propose to study the disintegration of measures along 1-dimensional subfoliations of the center bundle. Moreover, we obtain a more general result characterizing the disintegration of ergodic measures in our context.

arXiv comment15 pages, 2 figures

References in corpus (5)

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• Intrinsic ergodicity beyond specification: beta-shifts, S-gap shifts, and their factors
• Equilibrium measures for some partially hyperbolic systems
• On Equilibrium States for Partially Hyperbolic Horseshoes
• Invariance of entropy for maps isotopic to Anosov