Relativistic chaos in driven hamiltonian systems

Abstract

The relativistic classical dynamics of time-driven nonlinear Hamiltonian systems is investigated. The systems considered include the simple harmonic oscillator, the Duffing oscillator, the Morse oscillator, and a charged particle undergoing cyclotron motion. The nonlinearity arising from the relativistic kinetic energy term in the Hamiltonian serves as physical origins for complicated and stochastic behavior of the model systems. Particular attention is given to the resonance structure in the relativistic phase space of the driven nonlinear systems. It is shown that, when relativistic effects become appreciable, the resonances that exists in the nonrelativistic description can be shifted or suppressed and new resonances that do not exist in the nonrelativistic description can be generated in the high energy region. The overlap between these relativity-induced resonances can give rise to the onset of relativistic chaos. Also discussed is a relativistic oscillator whose period is independent of its energy. Theoretical and computational investigations of such a constant period oscillator are reported, with emphasis on basic mathematical and physical properties of the oscillator.