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

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  • 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.

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


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  •   M. Björklund, M. Einsiedler and A. Gorodnik, Quantitative Multiple Mixing, to appear in J. Eur. Math. Soc. (JEMS)
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