An integrable deformation of an ellipse of small eccentricity is an ellipse

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 eccent...

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Bibliographic Details
Published in:Annals of mathematics 2016-09, Vol.184 (2), p.527-558
Main Authors: Avila, Artur, De Simoi, Jacopo, Kaloshin, Vadim
Format: Article
Language:English
Subjects:
Billiards
Circles
Coordinate systems
Ellipses
Numerical eccentricity
Rotation
Sine function
Tangents
Trajectories
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Summary: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.
ISSN:0003-486X
DOI:10.4007/annals.2016.184.2.5