Dragović, Vladimir; Mironov, Andrey E. On differential equations of integrable billiard tables. (English) Zbl 07790989 Acta Math. Sin., Engl. Ser. 40, No. 1, 417-424 (2024). Reviewer: Daniel Jaud (München) MSC: 37C83 37J35 37J39 70H06 PDFBibTeX XMLCite \textit{V. Dragović} and \textit{A. E. Mironov}, Acta Math. Sin., Engl. Ser. 40, No. 1, 417--424 (2024; Zbl 07790989) Full Text: DOI arXiv
Bialy, Misha; Mironov, Andrey E. The Birkhoff-Poritsky conjecture for centrally-symmetric billiard tables. (English) Zbl 1505.37067 Ann. Math. (2) 196, No. 1, 389-413 (2022). Reviewer: William J. Satzer Jr. (St. Paul) MSC: 37J35 37J40 37J39 37J51 37C83 PDFBibTeX XMLCite \textit{M. Bialy} and \textit{A. E. Mironov}, Ann. Math. (2) 196, No. 1, 389--413 (2022; Zbl 1505.37067) Full Text: DOI arXiv
Bialy, Misha; Mironov, Andrey E.; Shalom, Lior Outer billiards with the dynamics of a standard shift on a finite number of invariant curves. (English) Zbl 1487.37031 Exp. Math. 30, No. 4, 469-474 (2021). MSC: 37C83 37J39 37J35 14H70 52C05 70K55 PDFBibTeX XMLCite \textit{M. Bialy} et al., Exp. Math. 30, No. 4, 469--474 (2021; Zbl 1487.37031) Full Text: DOI arXiv
Bialy, Misha; Mironov, Andrey E.; Shalom, Lior Magnetic billiards: non-integrability for strong magnetic field; Gutkin type examples. (English) Zbl 1464.37061 J. Geom. Phys. 154, Article ID 103716, 13 p. (2020). MSC: 37J40 37J30 37J35 PDFBibTeX XMLCite \textit{M. Bialy} et al., J. Geom. Phys. 154, Article ID 103716, 13 p. (2020; Zbl 1464.37061) Full Text: DOI arXiv
Bialy, Misha; Mironov, Andrey E.; Tabachnikov, Serge Wire billiards, the first steps. (English) Zbl 1477.37035 Adv. Math. 368, Article ID 107154, 26 p. (2020). MSC: 37C83 37J35 37J40 37D40 PDFBibTeX XMLCite \textit{M. Bialy} et al., Adv. Math. 368, Article ID 107154, 26 p. (2020; Zbl 1477.37035) Full Text: DOI arXiv
Bialy, M.; Mironov, A. E. Polynomial non-integrability of magnetic billiards on the sphere and the hyperbolic plane. (English. Russian original) Zbl 1439.37054 Russ. Math. Surv. 74, No. 2, 187-209 (2019); translation from Usp. Mat. Nauk 74, No. 2, 3-26 (2019). MSC: 37J30 37J35 37J38 37C83 PDFBibTeX XMLCite \textit{M. Bialy} and \textit{A. E. Mironov}, Russ. Math. Surv. 74, No. 2, 187--209 (2019; Zbl 1439.37054); translation from Usp. Mat. Nauk 74, No. 2, 3--26 (2019) Full Text: DOI arXiv
Bialy, Misha; Mironov, Andrey E. A survey on polynomial in momenta integrals for billiard problems. (English) Zbl 1407.37057 Philos. Trans. R. Soc. Lond., A, Math. Phys. Eng. Sci. 376, No. 2131, Article ID 20170418, 19 p. (2018). MSC: 37D50 PDFBibTeX XMLCite \textit{M. Bialy} and \textit{A. E. Mironov}, Philos. Trans. R. Soc. Lond., A, Math. Phys. Eng. Sci. 376, No. 2131, Article ID 20170418, 19 p. (2018; Zbl 1407.37057) Full Text: DOI arXiv
Bialy, Misha; Mironov, Andrey E. Angular billiard and algebraic Birkhoff conjecture. (English) Zbl 1364.37124 Adv. Math. 313, 102-126 (2017). MSC: 37J35 37D50 53A04 52A10 PDFBibTeX XMLCite \textit{M. Bialy} and \textit{A. E. Mironov}, Adv. Math. 313, 102--126 (2017; Zbl 1364.37124) Full Text: DOI arXiv
Agapov, S. V.; Bialy, M.; Mironov, A. E. Integrable magnetic geodesic flows on 2-torus: new examples via quasi-linear system of PDEs. (English) Zbl 1364.37123 Commun. Math. Phys. 351, No. 3, 993-1007 (2017). Reviewer: Jacques Franchi (Strasbourg) MSC: 37J35 37D40 53D25 PDFBibTeX XMLCite \textit{S. V. Agapov} et al., Commun. Math. Phys. 351, No. 3, 993--1007 (2017; Zbl 1364.37123) Full Text: DOI arXiv
Bialy, M.; Mironov, A. E. On fourth-degree polynomial integrals of the Birkhoff billiard. (English, Russian) Zbl 1371.37067 Proc. Steklov Inst. Math. 295, 27-32 (2016); translation in Tr. Mat. Inst. Steklova 295, 34-40 (2016). MSC: 37D50 14H70 PDFBibTeX XMLCite \textit{M. Bialy} and \textit{A. E. Mironov}, Proc. Steklov Inst. Math. 295, 27--32 (2016; Zbl 1371.37067); translation in Tr. Mat. Inst. Steklova 295, 34--40 (2016) Full Text: DOI
Bialy, Misha; Mironov, Andrey E. Integrable geodesic flows on 2-torus: formal solutions and variational principle. (English) Zbl 1304.53084 J. Geom. Phys. 87, 39-47 (2015). MSC: 53D25 35J62 37D40 PDFBibTeX XMLCite \textit{M. Bialy} and \textit{A. E. Mironov}, J. Geom. Phys. 87, 39--47 (2015; Zbl 1304.53084) Full Text: DOI arXiv