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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)
      M. Brin  and  Y. Pessin , Flows of frames on manifolds of negative curvature, Uspehi Mat. Nauk., 28 (1973) , 209-210. 
      M. Brin  and  Y. Pessin , Partially hyperbolic dynamical systems, Izv. Akad. Nauk SSSR Ser. Mat., 38 (1974) , 170-212. 
      T. Browning  and  Ilya Vinogradov , Effective Ratner theorem for $ {\rm{ASL}}(2, \mathbb{R})$ and gaps in $ \sqrt{n}$ modulo 1, J. London Math. Soc., 94 (2016) , 61-84. 
      S. G. Dani , Kolmogorov automorphisms on homogeneous spaces, Amer. J. Math., 98 (1976) , 119-163.  doi: 10.2307/2373618.
      S. G. Dani , Spectrum of an affine transformation, Duke Math. J., 44 (1977) , 129-155.  doi: 10.1215/S0012-7094-77-04407-6.
      D. Dolgopyat , Limit theorems for partially hyperbolic systems, Transactions of the American Mathematical Society, 356 (2004) , 1637-1689.  doi: 10.1090/S0002-9947-03-03335-X.
      D. Dolgopyat , On Decay of correlations in Anosov flows, Annals of Math., 147 (1998) , 357-390.  doi: 10.2307/121012.
      L. Flaminio  and  G. Forni , Invariant Distributions and Time Averages for Horocycle Flows, Duke J. of Math., 119 (2003) , 465-526.  doi: 10.1215/S0012-7094-03-11932-8.
      L. Flaminio and G. Forni, On effective equidistribution for higher step nilflows, arXiv:1407.3640
      L. Flaminio , G. Forni  and  J. Tanis , Effective equidistribution of twisted horocycle flows and horocycle maps, Geometric and Functional Analysis, 26 (5) , 1359-1448. 
      A. Gorodnik  and  R. Spatzier , Exponential mixing of nilmanifold automorphsims, Journal d'Analyse Methematique, 123 (2014) , 355-396.  doi: 10.1007/s11854-014-0024-7.
      D. Kelmer  and  P. Sarnak , Strong spectral gaps for compact quotients of products of $ {\rm{PSL}}(2, \mathbb R)$, J. Eur. Math. Soc., 11 (2009) , 283-313. 
      I. Konstantoulas , Effective decay of multiple correlations in semidirect product actions, Journal of Modern Dynamics, 10 (2016) , 81-111.  doi: 10.3934/jmd.2016.10.81.
      C. Liverani , On Contact Anosov flows, Annals of Math., 159 (2004) , 1275-1312.  doi: 10.4007/annals.2004.159.1275.
      E. Nelson , Analytic vectors, Annals of Math., 70 (1959) , 572-615.  doi: 10.2307/1970331.
      A. Strombergsson , An Effective Ratner Equidistribution Result for $ {\rm{SL}}(2,\mathbb R)\ltimes \mathbb R^2$, Duke Math. J., 164 (2015) , 843-902.  doi: 10.1215/00127094-2885873.
      J. Tanis  and  P. Vishe , Uniform bounds for period integrals and sparse equidistribution, International Mathematics Research Notices, (2015) , 13728-13756.  doi: 10.1093/imrn/rnv115.
      J. Tanis, Effective equidistribution for some unipotent flows in $ {\rm{PSL}}(2, \mathbb{R})^k$ mod cocompact irreducible lattice, arXiv:1412.5353v3
      A. Venkatesh , Sparse equidistribution problems, period bounds and subconvexity, Ann. of Math., 172 (2010) , 989-1094.  doi: 10.4007/annals.2010.172.989.
      I. Ilya Vinogradov, Effective equidistribution of horocycle lifts, arXiv:1607.04769
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