23 citations · 28 across the 10 of their papers we have counts for
11 papers
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…
Symmetric periodic orbits in symmetric billiards
Geraldo César Ferreira Gonçcalves, Sylvie Oliffson Kamphorst, Sônia Pinto-de-Carvalho
In this text we study billiards on ovals and investigate some consequences of a rotational symmetry of the boundary on the dynamics. As it simplifies some calculations, the symmetr…
Break-up of resonant invariant circles in perturbations of the geodesic circular billiard on surfaces of constant curvature
Luciano Coutinho dos Santos, Sônia Pinto-de-Carvalho
We study the non-persistence of horizontal invariant circles for geodesically convex perturbations of the geodesic circular billiard on surfaces of constant curvature and show that…
A Random Billiard Map in the Circle
Túlio Vales, Sônia Pinto-de-Carvalho
We consider a random billiard map, the one in which the standard specular reflection rule is replaced by a random reflection given by a Markov operator. We exhibit an invariant mea…
Modeling the prevalence of Schistosoma mansoni infection in an endemic population
Roberta Oliveira-Prado, Máderson Alvares de Souza Cabral, Sylvie Oliffson Kamphorst +3
We investigate theoretically if treatment alone can reduce the schistosomiasis's prevalence in an infected population, in a long-lasting sustainable way. We use a non-linear system…
Periodic Orbits of Oval Billiards on Surfaces of Constant Curvature
Luciano Coutinho dos Santos, Sonia Pinto-de-Carvalho
In this paper we define and study the billiard problem on bounded regions on surfaces of constant curvature. We show that this problem defines a 2-dimensional conservative and reve…
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…
Nonpersistence of resonant caustics in perturbed elliptic billiards
Sonia Pinto-de-Carvalho, Rafael Ramirez-Ros
Caustics are curves with the property that a billiard trajectory, once tangent to it, stays tangent after every reflection at the boundary of the billiard table. When the billiard…
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…
The First Birkhoff Coefficient and the Stability of 2-Periodic Orbits on Billiards
Sylvie Oliffson Kamphorst, Sonia Pinto de Carvalho
In this work we address the question of proving the stability of elliptic 2-periodic orbits for strictly convex billiards. Eventhough it is part of a widely accepted belief that el…