Rapid mixing and superpolynomial equidistribution for torus extensions of hyperbolic flows
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909909686157312 |
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| author | Zhang, Daofei |
| author_facet | Zhang, Daofei |
| contents | In this paper, we study mixing rates for $\mathbb{T}^{d}$-extensions of hyperbolic flows. Given three closed orbits with their holonomies, we can relate them to a point in $\mathbb{R}^{d+1}$. We prove that the extension flow enjoys rapid mixing, if the associated point is an inhomogeneously Diophantine number. Under the same assumption, we also obtain the superpolynomial equidistribution, namely, a superpolynomial error term in the equidistribution of the holonomy around closed orbits. Lastly, we apply these results to a class of three-dimensional frame flows. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_11367 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Rapid mixing and superpolynomial equidistribution for torus extensions of hyperbolic flows Zhang, Daofei Dynamical Systems In this paper, we study mixing rates for $\mathbb{T}^{d}$-extensions of hyperbolic flows. Given three closed orbits with their holonomies, we can relate them to a point in $\mathbb{R}^{d+1}$. We prove that the extension flow enjoys rapid mixing, if the associated point is an inhomogeneously Diophantine number. Under the same assumption, we also obtain the superpolynomial equidistribution, namely, a superpolynomial error term in the equidistribution of the holonomy around closed orbits. Lastly, we apply these results to a class of three-dimensional frame flows. |
| title | Rapid mixing and superpolynomial equidistribution for torus extensions of hyperbolic flows |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2405.11367 |