[۱] آقائی میبدی، فاطمه، ویژگیهایی از دینامیک بیلیارد، پایاننامۀ کارشناسی ارشد، دانشگاه یزد، ۱۳۹۹.
[2] Avila, A., De Simoi, J., Kaloshin, V., An integrable deformation of an ellipse of small eccentricity is an ellipse, Ann. of Math. (2), 184 (2016), 527-558.
[3] Aretxabaleta, X. M., Gonchenko, M., Harshman, N. L., Jackson, S. G., Olshanii, M., As-trakharchik, G. E., The dynamics of digits: Calculating pi with Galperin’s billiards, Mathematics, 8 (4) (2020), 509.
[4] Bialy, M., Convex billiards and a theorem by Hopf, Math. Z., 214 (2) (1993), 147-154.
[5] Birkhoff, G. D., Dynamical Systems, Amer. Math. Soc., Providence, RI, 1927.
[6] Bunimovich, L., On the ergodic properties of certain billiards, Funct. Anal. Appl., 8 (1974), 254255
[7] Cipra, B., Hanson, R., Kolan, E., Periodic trajectories in right-triangle billiards, Phys. Rev., E52 (1995), 2066-2071.
[8] Eskin, A., Mirzakhani, M., Mohammadi, A., Isolation, equidistribution, and orbit closures for the SL (2, R) action on Moduli space, Ann. of Math. (2), 182 (2015), 673-721.
[9] Fomenko, A. T., Mishchenko, A. S., A Short Course in Differential Geometry and Topology, Cambridge Scientific Publishers, New York, 2009.
[10] Galperin, G., Playing pool with π (the number π from a billiard point of view), Regul. Chaotic Dyn., 8 (2003), no. 4, 375-394.
[11] Gutkin, E., Billiard dynamics: An updated survey with the emphasis on open problems, Chaos, 22 (2012), 026116-1–026116-13.
[12] Gutkin, E., Billiards in polygons, Physica, D19 (1986), 311-333.
[13] Hezari, H., Zelditch, S., One can hear the shape of ellipses of small eccentricity, Ann. of Math. (2), 196 (2022), 1083-1134.
[14] Himmelstrand, M., Wilén, V., A survey of dynamical billiards, Technical report, Department of Mathematics, Royal Institute of Technology (KTH), 2013.
[15] Kaloshin, V., Sorrentino, A., On the local Birkhoff conjecture for convex billiards, Ann. of Math. (2), 188 (2018), 315-380.
[16] Masur, H., The growth rate of trajectories of a quadratic differential, Ergodic Theory Dynam. System, 10 (1990), 151-176.
[17] Masur, H., Lower bounds for the number of saddle connections and closed trajectories of a quadratic differential, in Holomorphic Functions and Moduli I, Mathematical Sciences Research Institute Publications, vol 10, Springer, New York, 1988, 215-228.
[18] Park, S. W., An introduction to dynamical billiards, available at https://math.uchicago.edu/may/REU2014/REUPapers/Park.pdf.
[19] Pecker, D., Poncelet's theorem and Billiard knots, Geom. Dedicata, 161 (1) (2012), 323-333.
[20] Poritsky, H., The billiard ball problem on a table with a convex boundary- An illustrative dynamical problem, Ann. of Math. (2), 51 (1955), 446-470.
[21] Tabachnikov, S., Billiards, Soc. Math. de France, Paris, 1995.
[22] Tabachnikov, S., Geometry and Billiards, Amer. Math. Soc., Providence, RI, 2005.
[23] Wright, A., From rational billiards to dynamics on moduli spaces, Bull. Amer. Math. Soc., 53 (1) (2015), 41-56.
