An application of lattice points counting to shrinking target problems

2017/01/16 by Dmitry Kleinbock, Xi Zhao, Kleinbock, Dmitry +1
Mathematics · Physics and Astronomy · #37A25 #37D40 #53D25 #Dynamical Systems (math.DS) #FOS: Mathematics #Geometry and complex manifolds #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.1701.04139

openalex publication_date 2017/01/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We apply lattice points counting results of Gorodnik and Nevo to solve a shrinking target problem in the setting of geodesic flows on hyperbolic manifolds of finite volume.

Related

• Shrinking targets for the geodesic flow on geometrically finite hyperbolic manifolds
• Shrinking targets for discrete time flows on hyperbolic manifolds
• A shrinking-target problem in the space of unimodular lattices in the three dimensional Euclidean space
• Counting problems from the viewpoint of ergodic theory: from primitive integer points to simple closed curves
• Discretely shrinking targets in moduli space