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arXiv · 2405.11367

Rapid mixing and superpolynomial equidistribution for torus extensions of hyperbolic flows

Daofei Zhang
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Abstract

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.

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Daofei Zhang. 2024-05-18. Rapid mixing and superpolynomial equidistribution for torus extensions of hyperbolic flows. https://arxiv.org/abs/2405.11367

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