Bouncing Outer Billiards
Dynamical Systems
2024-10-24 v1
Abstract
We introduce a new class of billiard-like system, ``bouncing outer billiards" which are 3-dimensional cousins of outer billiards of Neumann and Moser. We prove that bouncing outer billiard on a smooth convex body has at least four 1-parameter families of fixed points. We also fully describe dynamics of bouncing outer billiard on a line segment. Finally we carry out numerical experiments suggesting very complicated (non-ergodic) behavior for several shapes including the square and an ellipse.
Cite
@article{arxiv.2410.17985,
title = {Bouncing Outer Billiards},
author = {Andrey Gogolev and Levi Keck and Kevin Lewis},
journal= {arXiv preprint arXiv:2410.17985},
year = {2024}
}