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Cassaigne, J.; Hubert, Pascal; Troubetzkoy, Serge

Complexity and growth for polygonal billiards. (English) Zbl 1115.37312

Ann. Inst. Fourier 52, No. 3, 835-847 (2002).
Summary: 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.

Cited in 10 Documents

MSC:

37C35 Orbit growth in dynamical systems

Keywords:

complexity; polygonal billiards; generalized diagonals; bispecial words
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References:

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