Hölder Regularity and Exponential Decay of Correlations for a class of Piecewise Partially Hyperbolic Maps

Abstract

We consider a class of endomorphisms which contains a set of piecewise partially hyperbolic skew-products with a non-uniformly expanding base map. The aimed transformation preserves a foliation which is almost everywhere uniformly contracted with possible disconti- nuity sets, which are parallel to the contracting direction. We prove that the associated transfer operator, acting on suitable anisotropic normed spaces, has a spectral gap (on which we have quantitative estimation) and the disintegration of the unique invariant physical measure, along the stable leaves, is ζ-Hölder. We use this fact to obtain exponential decay of correlations on the set of ζ-Hölder functions.

Publication
Nonlinearity, 33(12), 6790. doi:10.1088/1361-6544/aba888

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