Calculations of Periodic Orbits for Hamiltonian Systems with Regularizable Singularities

摘要

We describe a numerical method for calculating periodic orbits, which is a generalization of the monodromy method by Baranger et al. to the case of an arbitrary autonomous dynamical system with a constant of motion C. By specifying the constant C to be the pseudoenergy , i.e. a value of the regularized Hamilton function, and applying the general method to the corresponding Hamilton’s equations, we show that this method can be used successfully for calculating periodic orbits of Hamiltonian systems having regularizable singularities in their original Hamilton functions.