E. Amiran, Caustics and evolutes for convex planar domains, J. Diff. Geometry, vol.28, pp.345-357, 1988.
DOI : 10.4310/jdg/1214442283
URL : https://doi.org/10.4310/jdg/1214442283

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. Bialy, Convex billiards and a theorem by E, Hopf. Math. Z, vol.214, issue.1, pp.147-154, 1993.
DOI : 10.1007/bf02572397

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.
DOI : 10.3934/dcds.2013.33.3903
URL : https://doi.org/10.3934/dcds.2013.33.3903

M. Bialy, On totally integrable magnetic billiards on constant curvature surface, Electron. Res. Announc. Math. Sci, vol.19, pp.112-119, 2012.
DOI : 10.3934/era.2012.19.112
URL : https://doi.org/10.3934/era.2012.19.112

M. Bialy and A. A. Mironov, Angular billiard and Angular Birkhoff Conjecture, Adv. in Math, vol.313, pp.102-126, 2017.
DOI : 10.1016/j.aim.2017.04.001
URL : http://arxiv.org/pdf/1601.03196

M. Bialy and A. Mironov, On fourth-degree polynomial integrals of the Birkhoff billiard, Proc. of Steklov Inst. of Math, vol.295, issue.1, pp.27-32, 2016.

M. Bialy and A. Mironov, Algebraic Birkhoff conjecture for billiards on Sphere and Hyperbolic plane, J. Geom. Phys, vol.115, pp.150-156, 2017.
DOI : 10.1016/j.geomphys.2016.04.017
URL : http://arxiv.org/pdf/1602.05698

P. Boyland, Dual billiards, twist maps and impact oscillators, Nonlinearity, vol.9, pp.1411-1438, 1996.
DOI : 10.1088/0951-7715/9/6/002
URL : http://arxiv.org/pdf/math/9408216

S. V. Bolotin, Integrable Birkhoff billiards. Mosc. Univ. Mech. Bull, vol.45, issue.2, pp.10-13, 1990.

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

E. Brieskorn and H. Knörrer, Plane algebraic curves, 1986.

A. Glutsyuk, On quadrilateral orbits in complex algebraic planar billiards, Moscow Math. J, vol.14, issue.2, pp.239-289, 2014.

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

A. Glutsyuk, On two-dimensional polynomially integrable Birkhoff billiards on surfaces of constant curvature

G. Greuel, C. Lossen, and E. Shustin, Introduction to singularities and deformations, 2007.

H. Hironaka, Arithmetic genera and effective genera of algebraic curves, Mem. Coll. Sci. Univ. Kyoto. Sect, vol.30, pp.177-195, 1956.

V. Kaloshin and A. Sorrentino, On local Birkhoff Conjecture for convex billiards

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.

J. Milnor, Singular points of complex hypersurfaces, 1968.

J. Moser, Is the solar system stable?, Math. Intell, vol.1, pp.65-71, 1978.

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.

E. Shustin, On invariants of singular points of algebraic curves, Math. Notes of Acad. Sci. USSR, vol.34, pp.962-963, 1983.

S. Tabachnikov, Billiards. Panor. Synth, vol.1, p.142, 1995.

S. Tabachnikov, Geometry and billiards. Student Mathematical Library 30, 2005.

S. Tabachnikov and F. Dogru, Dual billiards. Math. Intelligencer, vol.27, pp.18-25, 2005.

S. Tabachnikov, On algebraically integrable outer billiards, Pacific J. of Math, vol.235, issue.1, pp.101-104, 2008.

D. Treschev, Billiard map and rigid rotation, Phys. D, pp.31-34, 2013.

D. Treschev, On a Conjugacy Problem in Billiard Dynamics, Proc. Steklov Inst. Math, vol.289, issue.1, pp.291-299, 2015.

D. Treschev, A locally integrable multi-dimensional billiard system, Discrete Contin. Dyn. Syst, vol.37, issue.10, pp.5271-5284, 2017.

R. J. Walker, Algebraic Curves, 1978.

M. P. Wojtkowski, Two applications of Jacobi fields to the billiard ball problem, J. Differential Geom, vol.40, issue.1, pp.155-164, 1994.