Calculations of periodic orbits: The monodromy method and application to regularized systems.
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. Two variants of the method are developed, using the midpoint and the Runge-Kutta discretization of equations of motion, respectively. Particularly, we adapt the first variant for calculating periodic orbits of Hamiltonian systems when the period or the energy is given a priori. Finally, we consider the application of the monodromy method to the case of regularized mechanical systems and demonstrate the use by two examples. (c) 1999 American Institute of Physics.
Simonovic
N. S.
NS
Institute of Physics, P.O. Box 57, 11001 Belgrade, Yugoslavia.