Polygonal billiards with one side scattering
Alexandra Skripchenko (IMJ), Serge Troubetzkoy (FRUMAM, I2M)
TL;DR
This paper investigates the dynamics of polygonal billiards with a single vertical mirror on a square table, linking their trajectories to double rotations and exploring their complexity and orbit behavior.
Contribution
It introduces a novel model of polygonal billiards with one-sided scattering and analyzes their orbit structure and complexity using double rotation dynamics.
Findings
Trajectories can be characterized by double rotations.
Orbit behavior exhibits unique complexity patterns.
The study provides new insights into billiard dynamics with one-sided scattering.
Abstract
We study polygonal billiards with one-sided vertical mirror scattered on a square billiard table. We associate trajectories of these kinds of billiards with double rotations and study orbit behavior and questions of complexity.
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Taxonomy
TopicsQuantum chaos and dynamical systems · Mathematical Dynamics and Fractals · Advanced Differential Equations and Dynamical Systems