Abstract
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 very well understood.
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