arXiv subjects

Mario Jorge Dias Carneiro

Publications and source records attributed to Mario Jorge Dias Carneiro.

2 recordsLinked to original sources

arXiv2024

On the role of the surface geometry in convex billiards

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.

math.DS↗

arXiv2002

Elliptic Islands on Strictly Convex Billiards

This paper addresses the question of genericity of existence of elliptic islands for the billiard map associated to strictly convex closed curves. More precisely, we study 2-periodic orbits of billiards associated to C5 closed and strictly convex curves and show that the existence of elliptic islands is a dense property on the subset of those billiards having an elliptic 2-periodic point. Our main tools are normal perturbations, the Birkhoff Normal Form for elliptic fixed points and Moser's Twist Theorem.

math.DS↗