Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.11367 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of 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.