A proof of Culter's theorem on the existence of periodic orbits in polygonal outer billiards
Serge Tabachnikov
TL;DR
This paper discusses Culter's recent proof that all polygonal outer billiards possess at least one periodic trajectory, advancing understanding of dynamical behaviors in polygonal billiard systems.
Contribution
It presents a detailed analysis and proof of Culter's theorem confirming the existence of periodic orbits in polygonal outer billiards.
Findings
Proof of Culter's theorem established
Existence of periodic trajectories confirmed for all polygonal outer billiards
Enhances understanding of billiard dynamics in polygons
Abstract
We discuss a recent result by C. Culter: every polygonal outer billiard has a periodic trajectory.
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Taxonomy
TopicsQuantum chaos and dynamical systems · Mathematical Dynamics and Fractals · Advanced Differential Equations and Dynamical Systems