Sticky orbits of chaotic Hamiltonian dynamics

Nonuniformity of the phase space of chaotic Hamiltonian dynamics can result from the existence of a sticky set called “Sticky Riddle” (SR) imbedded into the phase space. Fractal and multifractal properties of SR can be described for some simplified situations. Existence of SR imposes similar stickiness for chaotic orbits when they approach the vicinity of SR. As a result, the orbits reveal behavior with power-like tails in the distribution of Poincare recurrences and exit times, which is unusual for hyperbolic systems. We exploit the generalized fractal dimension to describe the set of recurrences.