Partial Lyapunov exponents in tangent space dynamics

The authors have developed a new diagnostic tool for the analysis of the order-to-chaos transition: the partial Lyapunov exponents, defined through the dynamics in the tangent space. They allow the dynamics of single variables to be analysed, and are suitable for systems with several degrees of freedom. The authors have numerically simulated the dynamics of a model of five nonlinearly coupled oscillators; the partial Lyapunov exponents have been used to compute a characteristic coherence time for each degree of freedom. These quantities give information which is complementary to the usual statistical correlation times, and show that the high-frequency degrees of freedom, while losing their correlation during the order-to-chaos transition, may keep their coherence over long times.