6 papers
Lazutkin coordinates and the conjugation problem for billiard maps
Corentin Fierobe
The conjugation problem for billiard maps conjectures that if two strictly convex billiards have conjugated billiard maps, the billiard tables must be homothetic to each other. We…
Spectral rigidity among ellipses, Bialy's conjecture and local extrema of Mather's beta function
Corentin Fierobe
In this paper we prove Bialy's conjecture which states that if the Mather beta functions of two ellipses coincide at two nonzero rotation numbers then the ellipses coincide. We als…
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…
Rigidity of the Suris' potential in the Frenkel-Kontorova Model
Corentin Fierobe, Daniel Tsodikovich
The goal of this paper is to establish a local rigidity result for the integrability of standard-like maps. The main focus of the paper is the remarkable integrable potential disco…
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…
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…