The method of rational approximations: Periodic orbits and quasiperiodicity

In this study, we investigate rational approximate periodic solutions of nonlinear differential equations. We are especially interested to find simple formulae which can represent the main families of periodic orbits in a galactic model of two degrees of freedom. We also propose a new technique to represent quasiperiodic orbits and to follow the changes from periodicity to quasiperiodicity and vice-versa.