Comparison of convergence towards invariant distributions for rotation angles, twist angles and local Lyapunov characteristic numbers

Using the standard map as a model problem and in the spirit of cluster analysis we have studied the invariance of the distributions of different indicators introduced to detect and measure weak chaos. We show that the problem is less straightforward than expected and that, except for very strong chaotic dynamical systems, all the complexities (islands, sticking phenomena, cantori) of mixed Hamiltonian systems are reflected into the indicators of convergence towards invariant distributions.