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October  2007, 1(4): 649-663. doi: 10.3934/jmd.2007.1.649

Lower bounds on growth rates of periodic billiard trajectories in some irrational polygons

W. Patrick Hooper 1,

1. 

Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, IL, 60208-2730, United States

Received  April 2007 Revised  July 2007 Published  July 2007

In this paper we show that there exist irrational polygons $P$ where the number of periodic billiard paths of length less than $n$, $f_P(n)$, grows superlinearly. In fact, if we fix the number of sides of our polygon, for any $k \in \N$ there is an open set of polygons where $f_P(n)$ grows faster than $n \log^k n$.
Keywords: irrational billiards, periodic billiard paths..
Mathematics Subject Classification: Primary: 37D50; Secondary: 37E15, 37E3.
Citation: W. Patrick Hooper. Lower bounds on growth rates of periodic billiard trajectories in some irrational polygons. Journal of Modern Dynamics, 2007, 1 (4) : 649-663. doi: 10.3934/jmd.2007.1.649
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