Inhomogeneous Diophantine approximation and angular recurrence for polygonal billiards. (English. Russian original) Zbl 1043.37028

Sb. Math. 194, No. 2, 295-309 (2003); translation from Mat. Sb. 194, No. 2, 129-144 (2003).
By adapting and improving some dimensionality results in the theory of nonhomogeneous Diophantine approximations, centered around generalizations of Jarnik’s classic theorem, the authors prove strong recurrence properties in a class of polygonal billiards. This paper contains a well-organized survey of various results at the interface between the dynamics of billiards and number theory.


37D50 Hyperbolic systems with singularities (billiards, etc.) (MSC2010)
11J83 Metric theory
37A45 Relations of ergodic theory with number theory and harmonic analysis (MSC2010)
37C45 Dimension theory of smooth dynamical systems
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