Rapid mixing for compact group extensions of hyperbolic flows
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866908344496685056 |
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| author | Pollicott, Mark Zhang, Daofei |
| author_facet | Pollicott, Mark Zhang, Daofei |
| contents | In this article, we give explicit conditions for compact group extensions of hyperbolic flows (including geodesic flows on negatively curved manifolds) to exhibit quantifiable rates of mixing (or decay of correlations) with respect to the natural probability measures, which are locally the product of a Gibbs measure for a Hölder potential and the Haar measure. More precisely, we show that the mixing rate with respect to Hölder functions will be faster than any given polynomial (i.e., rapid mixing). We also give error estimates on the equidistribution of the holonomy around closed orbits. In particular, these results apply to some frame flows for manifolds with negative sectional curvatures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_07356 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Rapid mixing for compact group extensions of hyperbolic flows Pollicott, Mark Zhang, Daofei Dynamical Systems 37A25, 37C30, 37D20, 37D30, 37D40 In this article, we give explicit conditions for compact group extensions of hyperbolic flows (including geodesic flows on negatively curved manifolds) to exhibit quantifiable rates of mixing (or decay of correlations) with respect to the natural probability measures, which are locally the product of a Gibbs measure for a Hölder potential and the Haar measure. More precisely, we show that the mixing rate with respect to Hölder functions will be faster than any given polynomial (i.e., rapid mixing). We also give error estimates on the equidistribution of the holonomy around closed orbits. In particular, these results apply to some frame flows for manifolds with negative sectional curvatures. |
| title | Rapid mixing for compact group extensions of hyperbolic flows |
| topic | Dynamical Systems 37A25, 37C30, 37D20, 37D30, 37D40 |
| url | https://arxiv.org/abs/2405.07356 |