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arXiv · 2211.14737

Exponential mixing of frame flows for convex cocompact locally symmetric spaces

Michael Chow·Pratyush Sarkar
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Abstract

Let $G$ be a connected center-free simple real algebraic group of rank one and $\Gamma < G$ be a Zariski dense torsion-free convex cocompact subgroup. We prove that the frame flow on $\Gamma \backslash G$, i.e., the right translation action of a one-parameter subgroup $\{a_t\}_{t \in \mathbb R} < G$ of semisimple elements, is exponentially mixing with respect to the Bowen-Margulis-Sullivan measure. The key step is proving suitable generalizations of the local non-integrability condition and the non-concentration property which are essential for Dolgopyat's method. This generalizes the work of Sarkar-Winter for $G = \operatorname{SO}(n, 1)^\circ$ and also strengthens the mixing result of Winter in the convex cocompact case.

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Michael Chow, Pratyush Sarkar. 2022-11-27. Exponential mixing of frame flows for convex cocompact locally symmetric spaces. https://arxiv.org/abs/2211.14737

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