7 papers
Generic properties of planar symplectic billiards
Luca Baracco, Olga Bernardi, José Pedro Gaivão
We study generic properties of planar symplectic billiards, a symplectic analogue of classical Birkhoff billiards introduced by P. Albers and S. Tabachnikov. We prove that, for a r…
Birkhoff attractors for dissipative symplectic billiards
Luca Baracco, Olga Bernardi, Anna Florio +1
The aim of the present paper is to propose and study a dissipative variant of symplectic billiards within planar strictly convex domains. The associated billiard map is dissipative…
Starting the study of outer length billiards
Luca Baracco, Olga Bernardi, Corentin Fierobe
We focus on the outer length billiard dynamics, acting on the exterior of a strictly-convex planar domain. We first show that ellipses are totally integrable. We then provide an ex…
Area spectral rigidity for axially symmetric symplectic billiard tables
Luca Baracco, Olga Bernardi, Alessandra Nardi
We prove that any finitely smooth axially symmetric strictly convex domain, with everywhere positive curvature and sufficiently close to an ellipse is area spectrally rigid. This m…
Bialy-Mironov type rigidity for centrally symmetric symplectic billiards
Luca Baracco, Olga Bernardi, Alessandra Nardi
The aim of the present paper is to establish a Bialy-Mironov type rigidity for centrally symmetric symplectic billiards. For a centrally symmetric strongly-convex domain …
Birkhoff attractors of dissipative billiards
Olga Bernardi, Anna Florio, Martin Leguil
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…