Perturbation theory for nearly integrable systems

Abstract

Real dynamical systems are generally not integrable. In many cases the deviation of a system from an integrable one is small and can be considered as perturbation of the integrable system. To study perturbed systems special theoretical methods, known as perturbation theory, have been developed. They are based on the assumption that the solutions of a perturbed system are close to the corresponding solutions of the unperturbed (integrable) system, and one seeks the deviation of the perturbed solution from the unperturbed one as a series in the powers of a parameter which characterizes the strength of the perturbation. © 2006 Springer.