Dmitry Fuchs, Serge Tabachnikov, “Periodic trajectories in the regular pentagon, II”, Mosc. Math. J., 2013, Volume 13, Number 1,Pages <nobr>19

Periodic trajectories in the regular pentagon, II

Dmitry Fuchs^a, Serge Tabachnikov^b

^a Department of Mathematics, University of California, Davis, CA 95616, USA
^b Department of Mathematics, Pennsylvania State University, University Park, PA 16802, USA

Abstract: This paper is a continuation of our study of periodic billiard trajectories in the regular pentagon and closed geodesics on the double pentagon. The trajectories are encoded by infinite words in the alphabet consisting of five symbols. The main result of the paper is an algorithmic description of the symbolic periodic trajectories, conjectured in our recent paper.

Key words and phrases: translation surface, Veech surface, double pentagon, polygonal billiard, closed geodesic.

MSC: Primary 37D40; Secondary 37B10, 37E15, 37E35

Received: December 30, 2011; in revised form September 23, 2012

Language: English

DOI: 10.17323/1609-4514-2013-13-1-19-32