Birkhoff Conjecture for nearly centrally symmetric domains
| Autor: | Kaloshin, Vadim, Koudjinan, Comlan Edmond, Zhang, Ke |
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| Rok vydání: | 2023 |
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| Druh dokumentu: | Working Paper |
| Popis: | In this paper we prove a perturbative version of a remarkable Bialy-Mironov (Ann.Math:389-413(196), 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:389-413(196), 2022) with a local result by Kaloshin-Sorrentino (Ann.Math:315-380(188), 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:389-413(196), 2022) by proving that a notion of rational integrability is equivalent to the $C^0$-integrability condition used in their paper. Comment: Content and presentation improved. 40 pages |
| Databáze: | arXiv |
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