Exponential multiple mixing for some partially hyperbolic flows on products of $ {\rm{PSL}}(2, \mathbb{R})$

James Tanis

doi:10.3934/dcds.2018042

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2018, Volume 38, Issue 3: 989-1006. Doi: 10.3934/dcds.2018042

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Exponential multiple mixing for some partially hyperbolic flows on products of $ {\rm{PSL}}(2, \mathbb{R})$

James Tanis

Received: April 30, 2016

Revised: August 31, 2017

Published: June 2018

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Abstract

We prove a sharp estimate up to a logarithmic factor on the rate of equidistribution of coordinate horocycle flows on $ Γ \backslash{\rm{PSL}}(2, \mathbb{R})^d$, where $ d ∈ \mathbb{N}_{≥2}$ and $ Γ \subset {\rm{PSL}}(2, \mathbb{R})^d$ is a cocompact and irreducible lattice. As a consequence, we prove exponential multiple mixing for partially hyperbolic coordinate geodesic flows on these manifolds.

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Mathematics Subject Classification: Primary: 37A17, 37A25; Secondary: 37A45.

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