Geodesic
An integrable deformation of an ellipse of small eccentricity is an ellipse
Artur Avila1 ; Jacopo De Simoi2 ; Vadim Kaloshin3
1 CNRS, IMJ-PRG, UMR 7586, Université Paris Diderot, Sorbonne Paris Cité, Sorbonnes Universités, UPMC Univ Paris 06, Paris, France and IMPA, Rio de Janeiro, Brasil
2 University of Toronto, Toronto, ON, Canada
3 University of Maryland, College Park, MD
Annals of mathematics, Tome 184 (2016) no. 2, pp. 527-558.

Voir la notice de l'article provenant de la source Annals of Mathematics website

The classical Birkhoff conjecture claims that the boundary of a strictly convex integrable billiard table is necessarily an ellipse (or a circle as a special case). In this article we show that a version of this conjecture is true for tables bounded by small perturbations of ellipses of small eccentricity.
DOI : 10.4007/annals.2016.184.2.5

Artur Avila 1 ; Jacopo De Simoi 2 ; Vadim Kaloshin 3

1 CNRS, IMJ-PRG, UMR 7586, Université Paris Diderot, Sorbonne Paris Cité, Sorbonnes Universités, UPMC Univ Paris 06, Paris, France and IMPA, Rio de Janeiro, Brasil
2 University of Toronto, Toronto, ON, Canada
3 University of Maryland, College Park, MD 
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Artur Avila; Jacopo De Simoi; Vadim Kaloshin. An integrable deformation of an ellipse of small eccentricity is an ellipse. Annals of mathematics, Tome 184 (2016) no. 2, pp. 527-558. doi : 10.4007/annals.2016.184.2.5. http://geodesic.mathdoc.fr/articles/10.4007/annals.2016.184.2.5/

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