References
- [Avila et al. 16] A. Avila, J. De Simoi, and V. Kaloshin. “An Integrable Deformation of an Ellipse of Small Eccentricity is an Ellipse,” Ann. Math. 184:2 (2016), 527–558.
- [Bialy and Mironov nd] M. Bialy and A.E. Mironov. “Angular Billiard and Algebraic Birkhoff Conjecture.” Adv. Math. 313 (2017), 102–126.
- [Birkhoff 27] G. D. Birkhoff. Dynamical Systems, vol. 9. New YorkAmerican Mathematical Society Colloquium Publications, 1927.
- [Bolotin 90] S. V. Bolotin. “Integrable Birkhoff Billiards,” Vestnik Moskov. Univ. Ser. I Mat. Mekh. 2 (1990), 33–36, 105 (in Russian); translated in Mosc. Univ. Mech. Bull. 45:2 (1990), 10–13.
- [Bolotin 16] S. V. Bolotin. “Degenerate Billiards” Proc. Steklov Inst. Math. 295 (2016), 45–62.
- [Bolotin 15] S. V. Bolotin and D. V. Treschev. “The Anti-integrable Limit,” Russ. Math. Surv. 70:6 (2015), 975–1030.
- [Beauzamy et al. 90] B. Beauzamy, E. Bombieri, P. Enflo, and H. L. Montgomery. “Products of Polynomials in many Variables,” J. Number Theory 36:2 (1990), 219–245.
- [Delshams et al. 01] A. Delshams, Yu. Fedorov, and R. Ramirez-Ros. “Homoclinic Billiard Orbits Inside Symmetrically Perturbed Ellipsoids,” Nonlinearity 14:5 (2001), 1141–1195.
- [Dragovich and Radnovich 10] V. Dragovich and M. Radnovich. “Integrable Billiards and Quadrics,” Russ. Math. Surv. 65:2 (2010), 319–379.
- [Dragovich and Radnovich 11] V. Dragovich and M. Radnovich. “Poncelet Porisms and Beyond. Integrable Billiards, Hyperelliptic Jacobians and Pencils of Quadrics.” Frontiers in Mathematics, pp. viii+293. Basel: Birkhauser/Springer Basel AG, 2011.
- [Dragovich and Radnovich 15] V. Dragovich and M. Radnovich. “Pseudo-integrable Billiards and Double Reflection Nets,” Russ. Math. Surv. 70:1 (2015), 1–31.
- [Glutsyuk and Shustin nd] A. Glutsyuk and E. Shustin. “On Polynomially Integrable Planar Outer Billiards and Curves with Symmetry Property.” Preprint, arXiv:1607.07593.
- [Glutsyuk nd] A. Glutsyuk. “On Algebraically Integrable Birkhoff and Angular Billiards.” Preprint, arXiv:1706.04030.
- [Ivrii 80] V. Ja. Ivrii. “The Second Term of the Spectral Asymptotics for a Laplace-Beltrami Operator on Manifolds with Boundary,” Funktsional. Anal. i Prilozhen. 14:2 (1980), 25–34 (Russian).
- [Kaloshin and Sorrentino nd] V. Kaloshin and A. Sorrentino. “On Local Birkhoff Conjecture for Convex Billiards.” Preprint, arXiv:1612.09194.
- [Kozlov 16] V. V. Kozlov. “Polynomial Conservation Laws for the Lorentz Gas and the Boltzmann-Gibbs Gas,” Russ. Math. Surv. 71:2 (2016), 253–290.
- [Kozlov 91] V. V. Kozlov and D. V. Treschev Billiards. A Genetic Introduction to the Dynamics of Systems with Impacts, Translations of Mathematical Monographs 89. Providence, RI: American Mathematical Society, 1991.
- [Poritsky 50] H. Poritsky. “The Billiard Ball Problem on a Table with a Convex Boundary – An Illustrative Dynamical Problem,” Ann. Math. 51 (1950), 446–470.
- [Szasz 00] D. Szasz. “Boltzmann’s Ergodic Hypothesis, a Conjecture for Centuries?” In Hard Ball Systems and the Lorentz Gas, Encyclopaedia of Mathematical Sciences 101 (Mathematical Physics II), pp. 421–448. Berlin: Springer, 2000.
- [Tabachnikov 05] S. Tabachnikov. Geometry and Billiards, Student Mathematical Library 30. Providence, RIAmerican Mathematical Society, 2005.
- [Treschev 13] D. Treschev. “Billiard Map and Rigid Rotation,” Physica D 255 (2013), 31–34.
- [Treschev 15] D. V. Treschev. “On a Conjugacy Problem in Billiard Dynamics,” Proc. Steklov Inst. Math. 289 (2015), 291–299.
- [Treschev nd] D. Treschev. “A Locally Integrable Multi-dimensional Billiard System,” Discret. Contin. Dyn. Sys. – Ser. A 37:10, 5271–5284.
- [Whitney 34] H. Whitney. “Analytic Extensions of Functions Defined in Closed Sets,” Trans. Am. Math. Soc. 36:1 (1934), 63–89.