A. Avila, J. De-simoi, and V. Kaloshin, An integrable deformation of an ellipse of small eccentricity is an ellipse, Ann. of Math, issue.2, pp.527-558, 2016.

M. Berger, Seules les quadriques admettent des caustiques, Bull. Soc. Math. France, vol.123, pp.107-116, 1995.

M. Bialy, Convex billiards and a theorem by E, Hopf. Math. Z, vol.214, issue.1, pp.147-154, 1993.

M. Bialy, Hopf rigidity for convex billiards on the hemisphere and hyperbolic plane, Discrete Contin. Dyn. Syst, vol.33, issue.9, pp.3903-3913, 2013.

M. Bialy and A. Mironov, Angular billiard and algebraic Birkhoff conjecture, Adv. in Math, vol.313, pp.102-126, 2017.

M. Bialy and A. Mironov, Algebraic Birkhoff conjecture for billiards on Sphere and Hyperbolic plane, J. Geom. Phys, vol.115, pp.150-156, 2017.

M. Bialy and A. Mironov, A survey on polynomial in momenta integrals for billiard problems, Philos. Trans. Roy. Soc. A, vol.376, issue.2131, p.pp, 2018.

S. V. Bolotin, Integrable billiards on surfaces of constant curvature, Math. Notes, vol.51, issue.1-2, pp.117-123, 1992.

V. Dragovi? and M. Radnovi?, Integrable billiards and quadrics, Russian Math. Surveys, vol.65, issue.2, pp.319-379, 2010.

A. Glutsyuk, On 4-reflective complex analytic planar billiards, J. Geom. Analysis, pp.183-238, 2017.
URL : https://hal.archives-ouvertes.fr/ensl-01409258

A. A. Glutsyuk, On polynomially integrable billiards on surfaces of constant curvature, J. Eur. Math. Soc. Preprint
URL : https://hal.archives-ouvertes.fr/ensl-01664204

A. A. Glutsyuk, On two-dimensional polynomially integrable billiards on surfaces of constant curvature, Doklady Mathematics, vol.98, issue.1, pp.382-385, 2018.
URL : https://hal.archives-ouvertes.fr/ensl-01964938

V. Kaloshin and A. Sorrentino, On local Birkhoff Conjecture for convex billiards, Ann. of Math, vol.188, issue.1, pp.315-380, 2018.

V. Kaloshin and A. Sorrentino, On the integrability of Birkhoff billiards, Philos. Trans. Roy. Soc. A, vol.376, issue.2131, p.pp, 2018.

V. V. Kozlov, D. V. Treshchev, and . Billiards, A genetic introduction to the dynamics of systems with impacts, Translated from Russian by J.R.Schulenberger. Translations of Mathematical Monographs, vol.89, 1991.

H. Poritsky, The billiard ball problem on a table with a convex boundary -an illustrative dynamical problem, Ann. of Math, issue.2, pp.446-470, 1950.

O. Staude and . Iii, Quadriques. Encyclopédie des Sciences Mathématiques, Teubner, vol.22, 1904.

S. Tabachnikov, Geometry and Billiards, 2005.

S. Tabachnikov, Introducing projective billiards, Erg. Th. and Dynam. Sys, vol.17, pp.957-976, 1997.

S. Tabachnikov, Commuting dual billiard maps, Geometriae Dedicata, vol.53, pp.57-68, 1994.

A. P. Veselov, Integrable systems with discrete time, and difference operators, Funct. Anal. Appl, vol.22, issue.2, pp.83-93, 1988.

A. P. Veselov, Confocal surfaces and integrable billiards on the sphere and in the Lobachevsky space, J. Geom. Phys, vol.7, pp.81-107, 1990.