NONLINEAR RESONANCE AND CHAOS IN THE RELATIVISTIC PHASE-SPACE FOR DRIVEN NONLINEAR-SYSTEMS

Abstract

We investigate the relativistic dynamics of a time-driven nonlinear system by analyzing the resonance structure in the relativistic phase space. It is shown that, when relativistic effects become appreciable, resonances that exist in the nonrelativistic description may be shifted or suppressed and resonances that are absent in the nonrelativistic description may be induced to appear. When these relativity-induced resonances overlap, the system exhibits chaotic relativistic motion. Numerical data that demonstrate such relativistic effects are presented with model systems of the driven Duffing oscillator and the driven Morse oscillator.