Complexity and growth for polygonal billiards

Cassaigne, J.; Hubert, P.; Troubetzkoy, S.

Cassaigne, J. ; Hubert, P. ; Troubetzkoy, S.

HAL, hal-00133481 / Harvested from HAL

Résumé

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.

Publié le : 2002-07-05
Classification: [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS]

@article{hal-00133481,
     author = {Cassaigne, J. and Hubert, P. and Troubetzkoy, S.},
     title = {Complexity and growth for polygonal billiards},
     journal = {HAL},
     volume = {2002},
     number = {0},
     year = {2002},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00133481}
}

Cassaigne, J.; Hubert, P.; Troubetzkoy, S. Complexity and growth for polygonal billiards. HAL, Tome 2002 (2002) no. 0, . http://gdmltest.u-ga.fr/item/hal-00133481/