Computation of Invariant Tori and Acceleration of the K.A.M. Algorithm

摘要

A method is described to compute invariant tori in phase space for classical non-integrable Hamiltonian systems. The procedure is to solve the Hamilton-Jacobi equation stated as a system of equations for Fourier coefficients of the generating function. The system is truncated to a finite number of Fourier modes and solved numerically by Newton's Method. The resulting canonical transformation serves to reduce greatly the non-integrable part of the Hamiltonian. The method provides a promising alternative to canonical perturbation theory since its algebraic complexity does not increase as more accuracy is demanded and the required computer programs are quite simple. 2 refs., 1 fig. (ERA citation 11:006503)