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Recurrence and periodic billiard orbits in polygons. (English) Zbl 1049.37024

It is shown that almost all billiard trajectories return parallel to themselves for rank 1, ergodic polygons. Applications are given to the existence of periodic trajectories.

MSC:

37D50 Hyperbolic systems with singularities (billiards, etc.) (MSC2010)
37J10 Symplectic mappings, fixed points (dynamical systems) (MSC2010)
37A40 Nonsingular (and infinite-measure preserving) transformations
37C05 Dynamical systems involving smooth mappings and diffeomorphisms
37C27 Periodic orbits of vector fields and flows
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