Dynamical traps

We describe three types of dynamical traps in Hamiltonian systems which are due to the stickiness of trajectories to some specific domains in phase space. New estimates for the connection between Poincaré recurrence time distribution and transport exponents are presented. Particularly, the conditions are formulated for the ballistic transport in a finite-time simulation. We discuss a concept of pseudoergodicity in Hamiltonian chaotic dynamics and formulate a corresponding conjecture that the phenomenon of inequality of the time and ensemble averages in a finite-time simulation results in the existence of at least one of the described types of dynamical traps. The conjecture points to a “trouble” point in the theory of chaotic dynamics and, at the same time, shows new applications for the “cooling” of trajectories and synchronization of chaotic systems.