QUANTIFYING THE FOLDING MECHANISM IN CHAOTIC DYNAMICS

In this work we discuss different measures aimed to characterize the folding mechanism which together with the stretching process determine the chaotic dynamics. We show that from a study of the evolution of the distance between two trajectories beyond the exponential stage until the asymptotic regime is possible to obtain a quantity which provide an insight about this mechanism and its dependence on the control parameter. The asymptotic mean distance do manifests a specific power law dependence at the transition to chaos and is quite complementary to Lyapunov exponent in characterizing the chaotic motion. Then based on the methods of inverse statistics applied to one-dimensional maps we advance an alternative measure able to reflect the folding mechanism on the strange attractors. In the final part we argue briefly that the inverse statistics can be a relevant tool to the study of earthquakes produced in the Vrancea region.