Growth rates for geometric complexities and counting functions in polygonal billiards

Details Growth rates for geometric complexities and counting functions in polygonal billiards Growth rates for geometric complexities and counting functions in polygonal billiards

2007-04-16

arxiv.org/abs/0704.1975v1

Ergodic Theory & Dynamical Systems 29 (2009), 1163 -- 1183

Mathematics

Dynamical Systems

25 pages, 2 figures

Scientific paper

10.1017/S0143385708080620

We introduce a new method for estimating the growth of various quantities
arising in dynamical systems. We apply our method to polygonal billiards on
surfaces of constant curvature. For instance, we obtain power bounds of degree
two plus epsilon in length for the number of billiard orbits between almost all
pairs of points in a planar polygon.

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