  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.
