Artur Avila, Jacopo De Simoi, Vadim Kaloshin
Abstract
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The classical Birkhoff conjecture says that the only integrable convex domains are circles and ellipses. In the paper we show that this a version of this conjecture is true for small perturbations of ellipses of small eccentricity.
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The classical Birkhoff conjecture says that the only integrable convex domains are circles and ellipses. In the paper we show that this a version of this conjecture is true for small perturbations of ellipses of small eccentricity.
Key concepts: Ellipse, Eccentricity (behavior), Integrable system, Regular polygon, Conjecture, Geometry, Mathematics, Deformation (meteorology)