Frequency locking, Quasi periodicity and Chaos due to special relativistic effects

We study quasi periodic and frequency locked states that can occur in a sinusoidally driven linear harmonic oscillator in the special relativistic regime. We show how the shift in natural frequency of the oscillator with increasing relativistic effects leads to frequency locking or quasi periodicity and the chaotic states that arise due to the increasing non linearity. We find the same system can have multi-stable states in the presence of small damping. We also report an enhancement of chaos in the relativistic Henon-Heiles system.