Exponential mixing of frame flows for convex cocompact hyperbolic manifolds
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arXiv
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| Format: | Preprint |
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2020
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| _version_ | 1866914849433321472 |
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| author | Sarkar, Pratyush Winter, Dale |
| author_facet | Sarkar, Pratyush Winter, Dale |
| contents | The aim of this paper is to establish exponential mixing of frame flows for convex cocompact hyperbolic manifolds of arbitrary dimension with respect to the Bowen-Margulis-Sullivan measure. Some immediate applications include an asymptotic formula for matrix coefficients with an exponential error term as well as the exponential equidistribution of holonomy of closed geodesics. The main technical result is a spectral bound on transfer operators twisted by holonomy, which we obtain by building on Dolgopyat's method. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2004_14551 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Exponential mixing of frame flows for convex cocompact hyperbolic manifolds Sarkar, Pratyush Winter, Dale Dynamical Systems Differential Geometry Spectral Theory 37D40, 22E40, 37A25 The aim of this paper is to establish exponential mixing of frame flows for convex cocompact hyperbolic manifolds of arbitrary dimension with respect to the Bowen-Margulis-Sullivan measure. Some immediate applications include an asymptotic formula for matrix coefficients with an exponential error term as well as the exponential equidistribution of holonomy of closed geodesics. The main technical result is a spectral bound on transfer operators twisted by holonomy, which we obtain by building on Dolgopyat's method. |
| title | Exponential mixing of frame flows for convex cocompact hyperbolic manifolds |
| topic | Dynamical Systems Differential Geometry Spectral Theory 37D40, 22E40, 37A25 |
| url | https://arxiv.org/abs/2004.14551 |