Billiard Ordered Games and Books
Vladimir Dragovic, Sean Gasiorek, Milena Radnovic
TL;DR
This paper introduces a new class of integrable billiard systems by combining billiard ordered games with confocal billiard books, analyzing their dynamical and topological properties.
Contribution
It develops a novel approach to constructing integrable billiard systems using confocal billiard books and explores their dynamical and topological characteristics.
Findings
Construction of new integrable billiard domains
Analysis of dynamical properties of these systems
Topological classification of the configuration spaces
Abstract
The aim of this work is to put together two novel concepts from the theory of integrable billiards: billiard ordered games and confocal billiard books. Billiard books appeared recently in the work of Fomenko's school, in particular of V. Vedyushkina. These more complex billiard domains are obtained by gluing planar sets bounded by arcs of confocal conics along common edges. Such domains are used in this paper to construct the configuration space for billiard ordered games. We analyse dynamical and topological properties of the systems obtained in that way.
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