Relativistic nonlinear dynamics of a driven constant-period oscillator

Abstract

The nonlinear dynamics of the constant-period oscillator (relativistic oscillator whose period is independent of energy) driven by a time-periodic external force is studied. It is shown that the oscillator displays nonlinear resonances and chaos when the driving force is sufficiently strong. Such nonlinear behavior arises from the fact that the frequency of the oscillator is shifted from its natural value and becomes energy dependent in the presence of an external force. Theoretical analysis of the resonances is given using the second-order canonical perturbation theory.