Characterizing Weak Chaos using Time Series of Lyapunov Exponents

摘要

We investigate chaos in mixed-phase-space Hamiltonian systems using timeseries of the finite- time Lyapunov exponents. The methodology we propose usesthe number of Lyapunov exponents close to zero to define regimes of ordered(stickiness), semi-ordered (or semi-chaotic), and strongly chaotic motion. Thedynamics is then investigated looking at the consecutive time spent in eachregime, the transition between different regimes, and the regions in thephase-space associated to them. Applying our methodology to a chain of coupledstandard maps we obtain: (i) that it allows for an improved numericalcharacterization of stickiness in high-dimensional Hamiltonian systems, whencompared to the previous analyses based on the distribution of recurrencetimes; (ii) that the transition probabilities between different regimes aredetermined by the phase-space volume associated to the corresponding regions;(iii) the dependence of the Lyapunov exponents with the coupling strength.