Characterizing the dynamics of higher dimensional nonintegrable conservative systems

Abstract

The phase space dynamics of higher dimensional nonintegrable conservative systems is characterized via the effect of "sticky" motion on the finite time Lyapunov exponents (FTLEs) distribution. Since a chaotic trajectory suffers the sticky effect when chaotic motion is mixed to the regular one, it offers a way to separate the mixed from the totally chaotic regimes. To detect stickiness, four different measures are used, related to the distributions of the positive FTLEs, and provide conditions to characterize the dynamics. Conservative maps are systematically studied from the uncoupled two-dimensional case up to coupled maps of dimension 20. Sticky motion is detected in all unstable directions above a threshold K(d) of the nonlinearity parameter K for the high dimensional cases d = 10, 20. Moreover, as K increases we can clearly identify the transition from mixed to totally chaotic motion which occurs simultaneously in all unstable directions. Results show that all four statistical measures sensitively characterize the motion in high dimensional systems.