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"Sticky" motion in mixed phase space of conservative systems is difficult todetect and to characterize, in particular for high dimensional phase spaces.Its effect on quasi-regular motion is quantified here with four differentmeasures, related to the distribution of the finite time Lyapunov exponents. Westudy systematically standard maps from the uncoupled two-dimensional case upto coupled maps of dimension $20$. We find that sticky motion in all unstabledirections above a threshold $K_{d}$ of the nonlinearity parameter $K$ for thehigh dimensional cases $d=10,20$. Moreover, as $K$ increases we can clearlyidentify the transition from quasiregular to totally chaotic motion whichoccurs simultaneously in all unstable directions. The results show that allfour statistical measures sensitively probe sticky motion in high dimensionalsystems.

Footprints of sticky motion in the phase space of higher dimensional nonintegrable conservative systems