On Local Birkhoff Conjecture for Convex Billiards

@article{Kaloshin2016OnLB,
  title={On Local Birkhoff Conjecture for Convex Billiards},
  author={Vadim Kaloshin and Alfonso Sorrentino},
  journal={arXiv: Dynamical Systems},
  year={2016}
}
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 prove a local version of this conjecture: a small integrable perturbation of an ellipse must be an ellipse. This extends the result in [3], where only unperturbed ellipses of small eccentricities were considered. One of the crucial ideas in the proof is to extend action-angle coordinates for elliptic billiards… Expand

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