Complexity and growth for polygonal billiards
J. Cassaigne, Pascal Hubert, Serge Troubetzkoy (2002)
Annales de l’institut Fourier
Similarity:
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.