Hyperbolic Billiards (Autrans)

Hyperbolic Billiards

Liverani Carlangelo

Notes of the course
Some of the following notes are written very fast and are in an unstable form. In particular, several pictures are still missing. They are for the exlusive use of the students of the course. Read at your own risk.

  • General facts on how to establish hyperbolicity and billiards dynamics.
  • The standard reference for foliation regualrity is Hirsch, M. W.; Pugh, C. C.; Shub, M. Invariant manifolds. Lecture Notes in Mathematics, Vol. 583. Springer-Verlag, Berlin-New York, 1977. Unfortunately, it is not an easy reading. A quiker alternative presentaiton can be found in Appendix B of Anosov diffeomorphisms, anisotropic Banach spaces and regularity of foliations by Bahsoun, Liverani.
  • How to establish erdocity

    If you want to know more on Billiards the book to read is Chernov, Nikolai; Markarian, Roberto Chaotic billiards. Mathematical Surveys and Monographs, 127. American Mathematical Society, Providence, RI, 2006. Of course, some of the latest developements are missing, but it constitutes a wonerful starting point.

    If you want an introduction to various methods to study the startistical properties of hyperbolic dynamical systems you can have a look at the book Transfer operators in Hyperbolic Dynamics An introduction, Mark Demers, Niloofar Kiamari, Carlangelo Liverani. 33 Colloquio Brasilero de Matematica. Editora do IMPA. pp.252 (2021) and references therein.