52 citations · 80 across the 10 of their papers we have counts for
7 papers · 1 filter
Optical Billiards
Sylvie Oliffson Kamphorst, Sônia Pinto-de-Carvalho, Cássio Henrique Vieira Morais
This paper investigates the dynamics of optical billiards, a generalization of classic billiards, where light rays travel within a refractive medium and reflect elastically at the…
On the role of the surface geometry in convex billiards
Mario Jorge Dias Carneiro, Sylvie Oliffson Kamphorst, Sonia Pinto-de-Carvalho +1
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 whic…
Billiard dynamics near an invariant horizontal circle
Geraldo Cesar Goncalves Ferreira, Sylvie Oliffson Kamphorst, Sonia Pinto-de-Carvalho
Sufficiently differentiable oval billiards always have invariant rotational curves, but there are only two types of ovals with an invariant horizontal circle in its phase-space: th…
Limit Sets of Convex non Elastic Billiards
Roberto Markarian, Sylvie Oliffson Kamphorst, Sonia Pinto-de-Carvalho
Inspired by the work of Pujals and Sambarino on dominated splitting, we present billiards with a modified reflection law which constitute simple examples of dynamical systems with…
Generic Oval Billiards
M. J. Dias Carneiro, S. Oliffson Kamphorst, S. Pinto-de-Carvalho
In this paper we show that, under certain generic conditions, billiards on ovals have only a finite number of periodic orbits, for each period, all non-degenerate and at least one…
Elliptic Islands on Strictly Convex Billiards
Mario Jorge Dias Carneiro, Sylvie Oliffson Kamphorst, Sonia Pinto De Carvalho
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-period…
Elliptic Islands on the Elliptical Stadium
Sylvie Oliffson Kamphorst, Sonia Pinto de Carvalho
We investigate the existence of elliptic islands for a special family of periodic orbits of a two-parameter family of maps corresponding to the billiard problem on the elliptical s…