THE NONLOCAL OSCILLATOR

The most important characteristics of the son-local oscillator, an osc illator subjected to an additional non-local force, are extensively st udied by means of a new asymptotic perturbation method that is able to -furnish an approximate solution of weakly non-linear differential equ ations. The resulting motion is doubly periodic, because a second litt le frequency appears, in addition to the fundamental harmonic frequenc y. Comparison with the numerical solution obtained by the Runge-Kutta method confirms the validity of the asymptotic perturbation method and its importance for the study of non-linear dynamical systems.