Characterizing weak chaos in nonintegrable Hamiltonian systems: The fundamental role of stickiness and initial conditions

Weak chaos in high-dimensional conservative systems can be characterized through sticky effect induced by invariant structures on chaotic trajectories. Suitable quantities for this characterization are the higher cummulants of the finite time Lyapunov exponents (FTLEs) distribution. They gather the whole phase space relevant dynamics in one quantity and give information about ordered and random states. This is analyzed here for discrete Hamiltonian systems with local and global couplings. It is also shown that FTLEs plotted versus initial condition (IC) and the nonlinear parameter are essential to understand the fundamental role of ICs in the dynamics of weakly chaotic Hamiltonian systems.