Complexity and growth for polygonal billiards

2001/09/26 by J. Cassaigne, P. Hubert, S. Troubetzkoy
Mathematics · #math.DS #msc:37C

paper · pdf

published as Annales de l'Institut Fourier 52 (2002) 1001-1013. · 12 pages, 4 figures

arxiv created 2001/09/26 · arxiv updated 2009/11/30

Abstract

We establish a relationship between the word complexity and the number of generalized diagonals for a polygonal billiard. We conclude that in the rational case the complexity function has cubic upper and lower bounds. In the tiling case the complexity has cubic asymptotic growth.

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