@book{Pollard2002,
  author    = {Pollard, David},
  title     = {A User's Guide to Measure Theoretic Probability},
  series    = {Cambridge Series in Statistical and Probabilistic Mathematics},
  publisher = {Cambridge University Press},
  year      = {2002},
  isbn      = {978-0-521-00289-9},
  url       = {https://www.stat.yale.edu/~pollard/Books/UGMTP/}
}

@book{Durrett2019,
  author    = {Durrett, Rick},
  title     = {Probability: Theory and Examples},
  edition   = {Fifth},
  series    = {Cambridge Series in Statistical and Probabilistic Mathematics},
  volume    = {49},
  publisher = {Cambridge University Press},
  address   = {Cambridge},
  year      = {2019},
  isbn      = {978-1-108-47368-2},
  doi       = {10.1017/9781108591034},
  url       = {https://doi.org/10.1017/9781108591034}
}

@article{Birkhoff1927,
  author  = {Birkhoff, George D.},
  title   = {On the periodic motions of dynamical systems},
  journal = {Acta Mathematica},
  volume  = {50},
  pages   = {359--379},
  year    = {1927},
  doi     = {10.1007/BF02421325},
  url     = {https://doi.org/10.1007/BF02421325}
}

@article{Poritsky1950,
  author  = {Poritsky, Hillel},
  title   = {The billard ball problem on a table with a convex boundary---an illustrative dynamical problem},
  journal = {Annals of Mathematics},
  volume  = {51},
  number  = {2},
  pages   = {446--470},
  year    = {1950},
  doi     = {10.2307/1969334},
  url     = {https://www.jstor.org/stable/1969334}
}

@article{Lazutkin1973,
  author  = {Lazutkin, V. F.},
  title   = {The existence of caustics for a billiard problem in a convex domain},
  journal = {Mathematics of the USSR-Izvestiya},
  volume  = {7},
  number  = {1},
  pages   = {185--214},
  year    = {1973},
  doi     = {10.1070/IM1973v007n01ABEH001932},
  url     = {https://www.mathnet.ru/eng/im2221}
}

@article{MM1982,
  author  = {Marvizi, Shahla and Melrose, Richard},
  title   = {Spectral invariants of convex planar regions},
  journal = {Journal of Differential Geometry},
  volume  = {17},
  number  = {3},
  pages   = {475--502},
  year    = {1982},
  doi     = {10.4310/jdg/1214437138},
  url     = {https://doi.org/10.4310/jdg/1214437138}
}

@article{Mather1982,
  author  = {Mather, John N.},
  title   = {Glancing billiards},
  journal = {Ergodic Theory and Dynamical Systems},
  volume  = {2},
  number  = {3--4},
  pages   = {397--403},
  year    = {1982},
  doi     = {10.1017/S0143385700001681},
  url     = {https://doi.org/10.1017/S0143385700001681}
}

@article{Bialy1993,
  author  = {Bialy, Misha},
  title   = {Convex billiards and a theorem by {E. Hopf}},
  journal = {Mathematische Zeitschrift},
  volume  = {214},
  number  = {1},
  pages   = {147--154},
  year    = {1993},
  doi     = {10.1007/BF02572397},
  url     = {https://doi.org/10.1007/BF02572397}
}

@article{Innami2002,
  author  = {Innami, Nobuhiro},
  title   = {Geometry of geodesics for convex billiards and circular billiards},
  journal = {Nihonkai Mathematical Journal},
  volume  = {13},
  number  = {1},
  pages   = {73--120},
  year    = {2002},
  url     = {https://niigata-u.repo.nii.ac.jp/record/2183}
}

@article{AB2018,
  author  = {Arnold, Maxim and Bialy, Misha},
  title   = {Nonsmooth convex caustics for {Birkhoff} billiards},
  journal = {Pacific Journal of Mathematics},
  volume  = {295},
  number  = {2},
  pages   = {257--269},
  year    = {2018},
  doi     = {10.2140/pjm.2018.295.257},
  url     = {https://doi.org/10.2140/pjm.2018.295.257}
}

@article{BM2017,
  author  = {Bialy, Misha and Mironov, Andrey E.},
  title   = {Angular billiard and algebraic {Birkhoff} conjecture},
  journal = {Advances in Mathematics},
  volume  = {313},
  pages   = {102--126},
  year    = {2017},
  doi     = {10.1016/j.aim.2017.04.001},
  url     = {https://doi.org/10.1016/j.aim.2017.04.001}
}

@article{BM2022,
  author  = {Bialy, Misha and Mironov, Andrey E.},
  title   = {The {Birkhoff--Poritsky} conjecture for centrally-symmetric billiard tables},
  journal = {Annals of Mathematics},
  volume  = {196},
  number  = {1},
  pages   = {389--413},
  year    = {2022},
  doi     = {10.4007/annals.2022.196.1.2},
  url     = {https://annals.math.princeton.edu/2022/196-1/p02}
}

@article{Arnaud2009,
  author  = {Arnaud, Marie-Claude},
  title   = {Three results on the regularity of the curves that are invariant by an exact symplectic twist map},
  journal = {Publications Math{\'e}matiques de l'IH{\'E}S},
  volume  = {109},
  pages   = {1--17},
  year    = {2009},
  doi     = {10.1007/s10240-009-0017-8},
  url     = {https://doi.org/10.1007/s10240-009-0017-8}
}

@article{FS2026,
  author  = {Fierobe, Corentin and Sorrentino, Alfonso},
  title   = {On the existence of periodic invariant curves for analytic families of twist maps and billiards},
  journal = {Revista Matem{\'a}tica Iberoamericana},
  volume  = {42},
  number  = {1},
  pages   = {299--322},
  year    = {2026},
  doi     = {10.4171/RMI/1595},
  url     = {https://doi.org/10.4171/RMI/1595}
}

@article{ADK2016,
  author  = {Avila, Artur and De Simoi, Jacopo and Kaloshin, Vadim},
  title   = {An integrable deformation of an ellipse of small eccentricity is an ellipse},
  journal = {Annals of Mathematics},
  volume  = {184},
  number  = {2},
  pages   = {527--558},
  year    = {2016},
  doi     = {10.4007/annals.2016.184.2.5},
  url     = {https://annals.math.princeton.edu/2016/184-2/p05}
}

@article{KS2018,
  author  = {Kaloshin, Vadim and Sorrentino, Alfonso},
  title   = {On the local {Birkhoff} conjecture for convex billiards},
  journal = {Annals of Mathematics},
  volume  = {188},
  number  = {1},
  pages   = {315--380},
  year    = {2018},
  doi     = {10.4007/annals.2018.188.1.6},
  url     = {https://annals.math.princeton.edu/2018/188-1/p06}
}

@article{KKZ2024,
  author  = {Kaloshin, V. and Koudjinan, C. E. and Zhang, Ke},
  title   = {{Birkhoff} conjecture for nearly centrally symmetric domains},
  journal = {Geometric and Functional Analysis},
  volume  = {34},
  number  = {6},
  pages   = {1973--2007},
  year    = {2024},
  doi     = {10.1007/s00039-024-00695-6},
  url     = {https://link.springer.com/article/10.1007/s00039-024-00695-6}
}

@article{Koval2026,
  author  = {Koval, Illya},
  title   = {Local strong {Birkhoff} conjecture and local spectral uniqueness of almost every ellipse},
  journal = {Inventiones Mathematicae},
  volume  = {244},
  number  = {1},
  pages   = {221--298},
  year    = {2026},
  doi     = {10.1007/s00222-025-01397-y},
  url     = {https://link.springer.com/article/10.1007/s00222-025-01397-y},
  note    = {Published online 11 December 2025}
}

@article{Glutsyuk2026,
  author  = {Glutsyuk, A. A.},
  title   = {On complex algebraic caustics in planar and projective billiards},
  journal = {Regular and Chaotic Dynamics},
  volume  = {31},
  number  = {1},
  pages   = {132--149},
  year    = {2026},
  doi     = {10.1134/S1560354726010016},
  url     = {https://rcd.ics.org.ru/S1560354726010016/}
}

@book{Forster1981,
  author    = {Forster, Otto},
  title     = {Lectures on {Riemann} Surfaces},
  series    = {Graduate Texts in Mathematics},
  volume    = {81},
  publisher = {Springer-Verlag},
  address   = {New York},
  year      = {1981},
  note      = {Translated from the German by Bruce Gilligan},
  isbn      = {978-0-387-90617-1},
  doi       = {10.1007/978-1-4612-5961-9},
  url       = {https://link.springer.com/book/10.1007/978-1-4612-5961-9}
}

@book{Hormander1990,
  author    = {H{\"o}rmander, Lars},
  title     = {An Introduction to Complex Analysis in Several Variables},
  edition   = {Third},
  series    = {North-Holland Mathematical Library},
  volume    = {7},
  publisher = {North-Holland},
  address   = {Amsterdam},
  year      = {1990},
  isbn      = {978-0-444-88446-6}
}

@book{RevuzYor1999,
  author    = {Revuz, Daniel and Yor, Marc},
  title     = {Continuous Martingales and {Brownian} Motion},
  edition   = {Third},
  series    = {Grundlehren der mathematischen Wissenschaften},
  volume    = {293},
  publisher = {Springer-Verlag},
  address   = {Berlin},
  year      = {1999},
  isbn      = {978-3-540-64325-8},
  doi       = {10.1007/978-3-662-06400-9},
  url       = {https://link.springer.com/book/10.1007/978-3-662-06400-9}
}

@book{Garnett2007,
  author    = {Garnett, John B.},
  title     = {Bounded Analytic Functions},
  edition   = {Revised first},
  series    = {Graduate Texts in Mathematics},
  volume    = {236},
  publisher = {Springer},
  address   = {New York},
  year      = {2007},
  isbn      = {978-0-387-33621-3},
  doi       = {10.1007/0-387-49763-3},
  url       = {https://link.springer.com/book/10.1007/0-387-49763-3}
}

@misc{McMullen2017,
  author    = {McMullen, C.},
  title     = {Advanced Complex Analysis},
  year      = {2017},
  note      = {Harvard University Math 213a course notes, January 22, 2017},
  url       = {https://people.math.harvard.edu/~ctm/home/text/class/harvard/213a/10/html/home/course/course.pdf}
}