Hölder regularity and exponential decay of correlations for a class of piecewise partially hyperbolic maps
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| Format: | Preprint |
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2019
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| _version_ | 1866916699821834240 |
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| author | Bilbao, Rafael Bioni, Ricardo Lucena, Rafael |
| author_facet | Bilbao, Rafael Bioni, Ricardo Lucena, Rafael |
| contents | 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 discontinuity 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1911_06457 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Hölder regularity and exponential decay of correlations for a class of piecewise partially hyperbolic maps Bilbao, Rafael Bioni, Ricardo Lucena, Rafael Dynamical Systems 37A25, 37A10, 37C30, 37D50 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 discontinuity 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. |
| title | Hölder regularity and exponential decay of correlations for a class of piecewise partially hyperbolic maps |
| topic | Dynamical Systems 37A25, 37A10, 37C30, 37D50 |
| url | https://arxiv.org/abs/1911.06457 |