Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
149 tokens/sec
GPT-4o
9 tokens/sec
Gemini 2.5 Pro Pro
47 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Polynomial 3-mixing for smooth time-changes of horocycle flows (1909.08799v2)

Published 19 Sep 2019 in math.DS

Abstract: Let $(h_t){t\in \mathbb{R}}$ be the horocycle flow acting on $(M,\mu)=(\Gamma \backslash \text{SL}(2,\mathbb{R}),\mu)$, where $\Gamma$ is a co-compact lattice in $\text{SL}(2,\mathbb{R})$ and $\mu$ is the homogeneous probability measure locally given by the Haar measure on $\text{SL}(2,\mathbb{R})$. Let $\tau\in W6(M)$ be a strictly positive function and let $\mu{\tau}$ be the measure equivalent to $\mu$ with density $\tau$. We consider the time changed flow $(h_t\tau){t\in \mathbb{R}}$ and we show that there exists $\gamma=\gamma(M,\tau)>0$ and a constant $C>0$ such that for any $ f_0, f_1, f_2\in W6(M)$ and for all $0=t_0<t_1<t_2$, we have $$\ \left|\int_M \prod_{i=0}{2} f_i\circ h\tau_{t_i} d \mu\tau -\prod_{i=0}{2}\int_M f_i d \mu\tau \right|\leq C \left(\prod_{i=0}{2} |f_i|6\right) \left(\min{0\leq i<j\leq 2} |t_i-t_j|\right){-\gamma}.$$ With the same techniques, we establish polynomial mixing of all orders under the additional assumption of $\tau$ being fully supported on the discrete series.

Summary

We haven't generated a summary for this paper yet.