Periodic orbits in magnetic billiards

摘要

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 Poincare 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.