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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.

MSC:

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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