SELF-SIMILAR TRANSPORT IN INCOMPLETE CHAOS

Particle chaotic dynamics along a stochastic web is studied for three- dimensional Hamiltonian flow with hexagonal symmetry in a plane. Two d ifferent classes of dynamical motion, obtained by different values of a control parameter, and corresponding to normal and anomalous diffusi on, have been considered and compared. It is shown that the anomalous transport can be characterized by powerlike wings of the distribution function of displacement, flights which are similar to Levy flights, a pproximate trappings of orbits near the boundary layer of islands, and anomalous behavior of the moments of a distribution function consider ed as a function of the number of the moment. The main result is relat ed to the self-similar properties of different topological and dynamic al characteristics of the particle motion. This self-similarity appear s in the Weierstrass-like random-walk process that is responsible for the anomalous transport exponent in the mean-moment dependence on t. T his exponent can be expressed as a ratio of fractal dimensions of spac e and time sets in the Weierstrass-like process. An explicit form for the expression of the anomalous transport exponent through the local t opological properties of orbits has been given.