2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/123854The 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.13 pages, 40 figuresStatistical Mechanicstext