7 citations · 14 across the 15 of their papers we have counts for
15 papers
Rigidity of Mather's -function on a KAM set for analytic billiards-like maps and unique quasi-analytic continuation
Corentin Fierobe, Vadim Kaloshin, Frank Trujillo
In his seminal paper, Kac famously asked whether "one can hear the shape of a drum" - that is whether the isometry class of a bounded domain in a Euclidean space is uniquely determ…
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…
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…
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…
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…
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…
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…
Only quadrics have pseudo-caustics -- on caustics of Riemannian, pseudo-Euclidean and projective billiards in higher dimensions
Corentin Fierobe
This paper studies billiard models with a generalized law of reflection, the so-called projective billiards. They unify various laws, including the classical one in a Euclidean, ps…
Open problems on billiards and geometric optics
M. Bialy, C. Fierobe, A. Glutsyuk +3
This is a collection of open problems from workshop "Differential Geometry, Billiards, and Geometric Optics" at CIRM on October 4-8, 2021.
Thesis manuscript: Projective and complex billiards, periodic orbits and Pfaffian systems
Corentin Fierobe
This document is the manuscript of Corentin Fierobe's thesis about the billiard as a dynamical system. The first pages (title, introduction) are in French, but the rest of the docu…
On projective billiards with open subsets of triangular orbits
Corentin Fierobe
Ivrii's Conjecture states that in every billiard in Euclidean space the set of periodic orbits has measure zero. It implies that for every there are no k-reflective billia…
Examples of reflective projective billiards and outer ghost billiards
Corentin Fierobe
In the class of projective billiards, which contains the usual billiards, we exhibit counter-examples to Ivrii's conjecture, which states that in any planar billiard with smooth bo…
Complex caustics of the elliptic billiard
Corentin Fierobe
The article studies a generalization of the elliptic billiard to the complex domain. We show that the billiard orbits also have caustics, and that the number of such caustics is bi…
On the circumcenters of triangular orbits in elliptic billards
Corentin Fierobe
On an elliptic billard, we study a complex reflexion law introduced by A. Glutsyuk in order to state that the locus of the circumcenters of triangular orbits is an ellipse.