Troubetzkoy, Serge Recurrence and periodic billiard orbits in polygons. (English) Zbl 1049.37024 Regul. Chaotic Dyn. 9, No. 1, 1-12 (2004). 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. Reviewer: A. E. Mironov (Novosibirsk) Cited in 9 Documents 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 Keywords:billiard in a polygon; Poincaré recurrence theorem; angularly recurrent polygon; periodic orbit PDFBibTeX XMLCite \textit{S. Troubetzkoy}, Regul. Chaotic Dyn. 9, No. 1, 1--12 (2004; Zbl 1049.37024)