Characteristic times in the standard map.

We study and compare three characteristic times of the standard map: the Lyapunov time t_{L}, the Poincaré recurrence time t_{r}, and the stickiness (or escape) time t_{st}. The Lyapunov time is the inverse of the Lyapunov characteristic number (L) and in general is quite small. We find empirical relations for the L as a function of the nonlinearity parameter K and of the chaotic area A.

Global and local diffusion in the standard map.

We study the global and the local transport and diffusion in the case of the standard map, by calculating the diffusion exponent μ. In the global case, we find that the mean diffusion exponent for the whole phase space is either μ=1, denoting normal diffusion, or μ=2 denoting anomalous diffusion (and ballistic motion). The mean diffusion of the whole phase space is normal when no accelerator mode exists and it is anomalous (ballistic) when accelerator mode islands exist even if their area is tiny in the phase space.

Systems with escapes.

There are two types of escapes in conservative dynamical systems with two degrees of freedom: escapes to infinity and escapes to certain singular points at a finite distance. In both cases the areas on a surface of section are not preserved. We consider the basins of escape to infinity in simple Hamiltonian systems.