Complexity and growth for polygonal billiards

Details Complexity and growth for polygonal billiards Complexity and growth for polygonal billiards

2001-09-26

arxiv.org/abs/math/0109208v1

Annales de l'Institut Fourier 52 (2002) 1001-1013.

Mathematics

Dynamical Systems

12 pages, 4 figures

Scientific paper

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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