Chaotic lensed billiards
Timothy Chumley, Maeve Covey, Christopher Cox, Renato Feres

TL;DR
This paper introduces chaotic lensed billiards, a new class of dynamical systems with refraction effects, analyzing their properties through numerical experiments and switching dynamics between billiard subsystems.
Contribution
It extends classical billiard models by incorporating potential-induced refraction, providing a framework to analyze their chaotic behavior and dynamical properties.
Findings
Lyapunov exponents vary with potential parameter C
Lensed billiards exhibit switching dynamics between subsystems
Distinct properties from standard billiard systems
Abstract
Lensed billiards are an extension of the notion of billiard dynamical systems obtained by adding a potential function of the form , where is a real valued constant and is the indicator function of an open subset of the billiard table whose boundaries (of and the table) are piecewise smooth. Trajectories are polygonal lines that undergo either reflection or refraction at the boundary of depending on the angle of incidence. After laying out some basic concepts and general facts, in particular reviewing the optical/mechanical analogy that motivates these billiard models, we explore how their dynamical properties depend on the potential parameter using a number of families of examples. In particular, we explore numerically the Lyapunov exponents for these parametric families and highlight the more salient…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsQuantum chaos and dynamical systems · Chaos control and synchronization · Scientific Research and Discoveries
