Abstract:
A new class of integrable billiards is introduced, namely billiards with variable slipping. In such a system a particle occurring on the boundary slips along the boundary by an angle described by a function depending on the additional first integral. It is shown for such billiard systems in a disc that their isoenergy surfaces exhaust the set of manifolds with Heegaard genus 1. The homeomorphy class is described in terms of the set of solutions of a certain linear Diophantine equation in two variables.
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