| "Sticky" motion in mixed phase space of conservative systems is difficult to detect and to characterize, in particular for high dimensional phase spaces. Here, we study systematically standard maps beginning with the uncoupled two-dimensional case up to coupled maps of dimension d=20. For d>2 dimensional systems "sticky" motion can be interpreted as focusing of chaotic trajectories which influences the distribution of the finite time Lyapunov exponents qualitatively in the quasi-regular regime. This influence is quantified here with four variables: the variance (and the higher cumulants, skewness and kurtosis) and the normalized number of occurencies of the most probable finite time Lyapunov exponent (PΛ). Using these four variables we find that the effect of the focusing motion on the distributions of Lyapunov exponents is equal in different unstable directions above a threshold Kc 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 the four statistical variables are a sensitive probe for focusing motion in high dimensional systems. |
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