Strange kinetics

Hamiltonian energy conserving dynamical systems are examined and the problem of a kinetic description of dynamical systems with chaotic behavior is discussed. It is shown that simple nonlinearities in the Hamiltonian can induce fractal motions with nonstandard statistical properties or 'strange kinetics'. Topological properties of a phase-portrait of the system are discussed and strange kinetics rules are emphasized for Hamiltonian chaos. Scale invariant random walks are reviewed and stochastics and dynamics leading to time-dependent relationships are considered. Levy flights and walks relevant to dynamical systems whose orbits possess fractal properties are discussed. A phenomenology of a kinetic system undergoing strange kinetics with fractal properties is presented.