Uniqueness of Billiard Coding in Polygons
Yunzhe Li
TL;DR
This paper proves the uniqueness of coding for non-periodic billiard trajectories in polygons with holes of non-zero minimal diameter, extending previous results to a broader class of polygonal billiards.
Contribution
It generalizes a theorem by Galperin, Krüger, and Troubetzkoy to polygons with holes of non-zero minimal diameter, establishing new uniqueness results.
Findings
Proves uniqueness of coding in polygonal billiards with holes of minimal diameter
Extends previous theorems to more general polygonal billiard tables
Provides a broader understanding of billiard trajectory coding
Abstract
We consider polygonal billiards and we show the uniqueness of coding of non-periodic billiard trajectories in polygons whose holes have non-zero minimal diameters, generalising a theorem of Galperin, Kr\"uger and Troubetzkoy.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Quantum chaos and dynamical systems · Advanced Differential Equations and Dynamical Systems