26 citations · 64 across the 6 of their papers we have counts for
8 papers
Stochastic Perturbations of Convex Billiards
Roberto Markarian, Leonardo T. Rolla, Vladas Sidoravicius +2
We consider a strictly convex billiard table with boundary, with the dynamics subjected to random perturbations. Each time the billiard ball hits the boundary its reflection…
Exponential speed of mixing for skew-products with singularities
R. Markarian, M. J. Pacifico, J. Vieitez
Let be the endomorphism given by where is a positiv…
Structure and evolution of strange attractors in non-elastic triangular billiards
Aubin Arroyo, Roberto Markarian, David P. Sanders
We study pinball billiard dynamics in an equilateral triangular table. In such dynamics, collisions with the walls are non-elastic: the outgoing angle with the normal vector to the…
A local ergodic theorem for non-uniformly hyperbolic symplectic maps with singularities
Gianluigi Del Magno, Roberto Markarian
In this paper, we prove a criterion for the local ergodicity of non-uniformly hyperbolic symplectic maps with singularities. Our result is an extension of a theorem of Liverani and…
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…
Mixing rate for semi-dispersing billiards with non-compact cusps
A. Arbieto, R. Markarian, M. J. Pacifico +1
Since the seminal work of Sinai one studies chaotic properties of planar billiards tables. Among them is the study of decay of correlations for these tables. There are examples in…
Bifurcations of periodic and chaotic attractors in pinball billiards with focusing boundaries
Aubin Arroyo, Roberto Markarian, David P. Sanders
We study the dynamics of billiard models with a modified collision rule: the outgoing angle from a collision is a uniform contraction, by a factor lambda, of the incident angle. Th…
Chaotic Properties of the Elliptical Stadium
Roberto Markarian, Sylvie Oliffson Kamphorst, Sonia Pinto de Carvalho
The elliptical stadium is a curve constructed by joining two half-ellipses, with half axes a>1 and b=1, by two straight segments of equal length 2h. In this work we find bounds on…