An integrable deformation of an ellipse of small eccentricity is an ellipse
By Artur Avila, J. Simoi, Vadim Kaloshin. 2014
98 citations recorded by the source corpus.
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.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/0a8b6e5e0d53d94f80c4b4b5cde0cce896f8105e
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- On the local Birkhoff conjecture for convex billiards (2016, methodology): “[21] Guan Huang, Vadim Kaloshin and Alfonso Sorrentino On Strong Local Birkhoff conjecture near ellipses of small eccentricity.”