@article{18483,
  abstract     = {In this paper we prove a perturbative version of a remarkable Bialy–Mironov (Ann. Math. 196(1):389–413, 2022) result. They prove non perturbative Birkhoff conjecture for centrally-symmetric convex domains, namely, a centrally-symmetric convex domain with integrable billiard is ellipse. We combine techniques from Bialy–Mironov (Ann. Math. 196(1):389–413, 2022) with a local result by Kaloshin–Sorrentino (Ann. Math. 188(1):315–380, 2018) and show that a domain close enough to a centrally symmetric one with integrable billiard is ellipse. To combine these results we derive a slight extension of Bialy–Mironov (Ann. Math. 196(1):389–413, 2022) by proving that a notion of rational integrability is equivalent to the C0-integrability condition used in their paper.},
  author       = {Kaloshin, Vadim and Koudjinan, Edmond and Zhang, Ke},
  issn         = {1420-8970},
  journal      = {Geometric and Functional Analysis},
  pages        = {1973--2007},
  publisher    = {Springer Nature},
  title        = {{Birkhoff conjecture for nearly centrally symmetric domains}},
  doi          = {10.1007/s00039-024-00695-6},
  volume       = {34},
  year         = {2024},
}