An application of lattice points counting to shrinking target problems

DOI10.3934/dcds.2018007zbMath1372.37067arXiv1701.04139OpenAlexW2572654949MaRDI QIDQ2409071

Xi Zhao, Dmitry Kleinbock

Publication date: 10 October 2017

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1701.04139

zbMATH Keywords

geodesic flowshyperbolic geometrycounting of lattice pointsshrinking target problems

Mathematics Subject Classification ID

Ergodicity, mixing, rates of mixing (37A25) Geodesic flows in symplectic geometry and contact geometry (53D25) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40)

Related Items (8)

Shrinking targets for the geodesic flow on geometrically finite hyperbolic manifolds ⋮ Multiple Borel-Cantelli lemma in dynamics and multilog law for recurrence ⋮ Discretely shrinking targets in moduli space ⋮ Shrinking targets for discrete time flows on hyperbolic manifolds ⋮ Extreme value distributions for one-parameter actions on homogeneous spaces ⋮ An inhomogeneous Dirichlet theorem via shrinking targets ⋮ Geometric and measure-theoretic shrinking targets in dynamical systems ⋮ Shrinking target problems for flows on homogeneous spaces

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• The rate of mixing for geodesic and horocycle flows
• Limit theorems for partially hyperbolic systems
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• Dynamical Borel-Cantelli lemmas for Gibbs measures

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