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Pseudo-integrable billiards Dragovic, Vladimir


We present a class of nonconvex billiards with a boundary composed of arcs of confocal conics which contain reflex (nonconvex) angles. We present their basic dynamical, topological, and arithmetic properties. Such systems are not integrable, but carry strong traces of integrability. We study their periodic orbits and establish a local Poncelet porism. A connection with interval exchange transformation is established together with the Keane-type conditions for minimality. A transformation from pseudo-integrable billiards to rectangular billiards is constructed. This research is done jointly with M. Radnovic.

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