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arXiv · 1508.03858

Generic Absence of Finite Blocking for Interior Points of Birkhoff Billiards

Thomas Dauer·Marlies Gerber
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Abstract

Let x and y be points in a billiard table M that is bounded by a curve sigma. We assume that sigma is a simple closed C^r curve with positive curvature, where r is at least 2. A subset B of M\{x,y} is called a blocking set for the pair (x,y) if every billiard path in M from x to y passes through a point in B. If a finite blocking set exists, the pair (x,y) is called secure in M; if not, it is called insecure. We show that for the generic (in the sense of Baire category) curve sigma, the generic pair of interior points is insecure.

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Thomas Dauer, Marlies Gerber. 2015-08-16. Generic Absence of Finite Blocking for Interior Points of Birkhoff Billiards. https://arxiv.org/abs/1508.03858

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