4 papers · 1 filter
Unbounded orbits in -generic centrally symmetric strictly convex outer billiards
Alfonso Sorrentino
Let be the space of support functions of centrally symmetric, strictly convex, compact planar bodies whose boundary is a curve, endowed with the topology.…
A billiard table close to an ellipse is deformationally spectrally rigid among dihedrally symmetric domains
Corentin Fierobe, Vadim Kaloshin, Alfonso Sorrentino
We prove that a a strongly convex planar domain (Birkhoff table) with dihedral symmetry, which is sufficiently close in a finitely smooth topology to an ellipse, is deformationally…
Deformational spectral rigidity of axially-symmetric symplectic billiards
Corentin Fierobe, Alfonso Sorrentino, Amir Vig
Symplectic billiards were introduced by Albers and Tabachnikov as billiards in strictly convex bounded domains of the plane with smooth boundary having a specific law of reflection…
On the existence of periodic invariant curves for analytic families of twist maps and billiards
Corentin Fierobe, Alfonso Sorrentino
In this paper we prove that in any analytic one-parameter family of twist maps of the annulus, homotopically invariant curves filled with periodic points corresponding to a given r…