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Weak chaos in high-dimensional conservative systems can be characterizedthrough sticky effect induced by invariant structures on chaotic trajectories.Suitable quantities for this characterization are the higher cummulants of thefinite time Lyapunov exponents (FTLEs) distribution. They gather the {\itwhole} phase space relevant dynamics in {\it one} quantity and giveinformations about ordered and random states. This is analyzed here fordiscrete Hamiltonian systems with local and global couplings. It is also shownthat FTLEs plotted {\it versus} initial condition (IC) and the nonlinearparameter is essential to understand the fundamental role of ICs in thedynamics of weakly chaotic Hamiltonian systems.

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