Circular billiards and parallel axiom in convex billiards
Nobuhiro Innami and Shinetsu Tamura
Source: Tsukuba J. Math. Volume 33, Number 1
(2009), 147-160.
Abstract
Circles will be characterized by some properties of billiard ball trajectories. The theory of parallels and the parallel axiom play important roles in the geometry of the configuration space. Those characterizations are concerned with Bialy's theorem which is a partial answer to Birkhoff's conjecture.
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