Polygonal symplectic billiards
Peter Albers, Gautam Banhatti, Filip Sadlo, Richard Schwartz, Serge, Tabachnikov
TL;DR
This paper investigates polygonal symplectic billiards, presenting new theoretical results and conjectures inspired by numerical experiments, including polygons with exclusively periodic orbits.
Contribution
It introduces novel findings on polygonal symplectic billiards, especially polygons with all orbits periodic, supported by numerical methods.
Findings
Identified polygons with all orbits periodic
Developed two numerical implementations for analysis
Proposed conjectures based on numerical observations
Abstract
In this article, we study polygonal symplectic billiards. We provide new results, some of which are inspired by numerical investigations. In particular, we present several polygons for which all orbits are periodic. We demonstrate their properties and derive various conjectures using two numerical implementations.
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Taxonomy
TopicsQuantum chaos and dynamical systems · Mathematical Dynamics and Fractals · Cellular Automata and Applications