---
res:
  bibo_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.@eng
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Vadim
      foaf_name: Kaloshin, Vadim
      foaf_surname: Kaloshin
      foaf_workInfoHomepage: http://www.librecat.org/personId=FE553552-CDE8-11E9-B324-C0EBE5697425
    orcid: 0000-0002-6051-2628
  - foaf_Person:
      foaf_givenName: Edmond
      foaf_name: Koudjinan, Edmond
      foaf_surname: Koudjinan
      foaf_workInfoHomepage: http://www.librecat.org/personId=52DF3E68-AEFA-11EA-95A4-124A3DDC885E
    orcid: 0000-0003-2640-4049
  - foaf_Person:
      foaf_givenName: Ke
      foaf_name: Zhang, Ke
      foaf_surname: Zhang
  bibo_doi: 10.1007/s00039-024-00695-6
  bibo_volume: 34
  dct_date: 2024^xs_gYear
  dct_identifier:
  - UT:001329804200001
  dct_isPartOf:
  - http://id.crossref.org/issn/1016-443X
  - http://id.crossref.org/issn/1420-8970
  dct_language: eng
  dct_publisher: Springer Nature@
  dct_title: Birkhoff conjecture for nearly centrally symmetric domains@
...