4 papers
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…
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 …
Higher order terms of Mather's -function for symplectic and outer billiards
Luca Baracco, Olga Bernardi, Alessandra Nardi
We compute explicitly the higher order terms of the formal Taylor expansion of Mather's -function for symplectic and outer billiards in a strictly-convex planar domain . In p…