Footprints of sticky motion in the phase space of higher dimensional nonintegrable conservative systems
Abstract
"Sticky" motion in mixed phase space of conservative systems is difficult to detect and to characterize, in particular for high dimensional phase spaces. Its effect on quasi-regular motion is quantified here with four different measures, related to the distribution of the finite time Lyapunov exponents. We study systematically standard maps from the uncoupled two-dimensional case up to coupled maps of dimension 20. We find that sticky motion in all unstable directions above a threshold Kd of the nonlinearity parameter K for the high dimensional cases d=10,20. Moreover, as K increases we can clearly identify the transition from quasiregular to totally chaotic motion which occurs simultaneously in all unstable directions. The results show that all four statistical measures sensitively probe sticky motion in high dimensional systems.