Exterior differential systems and billiards. (English) Zbl 1105.58003

Landsberg, Joseph M.

Mladenov, Ivaïlo (ed.) et al., Proceedings of the 7th international conference on geometry, integrability and quantization, Sts. Constantine and Elena, Bulgaria, June 2–10, 2005. Sofia: Bulgarian Academy of Sciences (ISBN 954-8495-30-9/pbk). 35-54 (2006).

The aim of this note is to introduce the techniques of exterior differential systems in the context of a problem in billiards. The author generally works in the real analytic category, although all the nonexistence results discussed in the paper imply nonexistence of smooth solutions.
For the entire collection see [Zbl 1089.53004].

Reviewer: Messoud A. Efendiev (Berlin)

MSC:

58A15	Exterior differential systems (Cartan theory)
35P05	General topics in linear spectral theory for PDEs
37D50	Hyperbolic systems with singularities (billiards, etc.) (MSC2010)
37J99	Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems

Keywords:

billiards; exterior differential systems; real analytic category