Limit sets of convex non-elastic billiards

Markarian, Roberto; Kamphorst, Sylvie Oliffson; Pinto-de-Carvalho, Sônia

doi:10.1080/14689367.2012.669468

Dynamical Systems

2012

DOI: 10.1080/14689367.2012.669468

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Limit sets of convex non-elastic billiards

Roberto Markarian

Sylvie Oliffson Kamphorst

Sônia Pinto-de-Carvalho

Abstract: Inspired by the work of Pujals and Sambarino on dominated splitting [20], we present billiards with a modified reflection law which constitute simple examples of dynamical systems with limit sets having dominated splitting and where the dynamics is a rational or irrational rotation.

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2024

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Birkhoff attractors of dissipative billiards

BERNARDI,

FLORIO,

LEGUIL

2024

Ergod. Th. Dynam. Sys.

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We study the dynamics of dissipative billiard maps within planar convex domains. Such maps have a global attractor. We are interested in the topological and dynamical complexity of the attractor, in terms both of the geometry of the billiard table and of the strength of the dissipation. We focus on the study of an invariant subset of the attractor, the so-called Birkhoff attractor. On the one hand, we show that for a generic convex table with ‘pinched’ curvature, the Birkhoff attractor is a normally contracted manifold when the dissipation is strong. On the other hand, for a mild dissipation, we prove that, generically, the Birkhoff attractor is complicated, both from the topological and the dynamical points of view.

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Birkhoff attractors of dissipative billiards

BERNARDI,

FLORIO,

LEGUIL

2024

Ergod. Th. Dynam. Sys.

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Limit sets of convex non-elastic billiards

Abstract: Inspired by the work of Pujals and Sambarino on dominated splitting [20], we present billiards with a modified reflection law which constitute simple examples of dynamical systems with limit sets having dominated splitting and where the dynamics is a rational or irrational rotation.

Cited by 1 publication

References 16 publications

Birkhoff attractors of dissipative billiards

Birkhoff attractors of dissipative billiards

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