2009, 3(2): 159-231. doi: 10.3934/jmd.2009.3.159

Billiards in nearly isosceles triangles

1. 

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

2. 

Department of Mathematics, Brown University, Providence, RI 02912, United States

Received  July 2008 Published  May 2009

We prove that any sufficiently small perturbation of an isosceles triangle has a periodic billiard path. Our proof involves the analysis of certain infinite families of Fourier series that arise in connection with triangular billiards, and reveals some self-similarity phenomena in irrational triangular billiards. Our analysis illustrates the surprising fact that billiards on a triangle near a Veech triangle is extremely complicated even though billiards on a Veech triangle is well understood.
Citation: W. Patrick Hooper, Richard Evan Schwartz. Billiards in nearly isosceles triangles. Journal of Modern Dynamics, 2009, 3 (2) : 159-231. doi: 10.3934/jmd.2009.3.159
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