Periodic orbits in magnetic billiards
Instituto de Física "Gleb Wataghin", Universidade Estadual de Campinas (UNICAMP), Caixa
13083-970 Campinas, Brazil
Revised: 13 April 2000
Published online: 15 August 2000
We propose a simple method to calculate periodic orbits in two-dimensional systems with no symbolic dynamics. The method is based on a line by line scan of the Poincaré surface of section and is particularly useful for billiards. We have applied it to the Square and Sinai's billiards subjected to a uniform orthogonal magnetic field and we obtained about 2000 orbits for both systems using absolutely no information about their symbolic dynamics.
PACS: 05.45.-a – Nonlinear dynamics and nonlinear dynamical systems / 05.45.Pq – Numerical simulations of chaotic models / 05.45.Mt – Semiclassical chaos ("quantum chaos")
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2000