Nonintegrability and fluctuation by symmetry violation in perturbed harmonic oscillator systems

Abstract

The violation of symmetry between the time series of elongation and contraction rates of phase-space point spacings is studied to examine the chaos in perturbed harmonic oscillator systems. A transition from integrability to nonintegrability is quantitatively evaluated by introducing a correlation coefficient for the degree of symmetry violation. A feature of the correlation coefficient is discussed, suggesting a possible advantage over the Lyapunov exponent. The relationship between a fluctuation property based on symmetry violation and nonintegrability is also discussed.