On the role of the surface geometry in convex billiards
Dynamical Systems
2024-09-19 v3
Abstract
This work presents a framework for billiards in convex domains on two dimensional Riemannian manifolds. These domains are contained in connected, simply connected open subsets which are totally normal. In this context, some basic properties that have long been known for billiards on the plane are established. We prove the twist property and investigate conditions on the billiard for the existence and non existence of rotational invariant curves.
Cite
@article{arxiv.2308.14856,
title = {On the role of the surface geometry in convex billiards},
author = {Mario Jorge Dias Carneiro and Sylvie Oliffson Kamphorst and Sonia Pinto-de-Carvalho and Cassio Henrique Vieira Morais},
journal= {arXiv preprint arXiv:2308.14856},
year = {2024}
}
Comments
We changed the title, from "The Twist Property and the Existence of Invariant Curves for Convex Billiards on Surfaces" to "On the role of the surface geometry in convex billiards"