FRACTIONAL KINETIC-EQUATION FOR HAMILTONIAN CHAOS

Hamiltonian chaotic dynamics of particles (or passive particles in fluids) can be described by a fractional generalization of the Fokker-Planck-Kolmogorov equation (FFPK) which is defined by two fractional critical exponents (alpha, beta) responsible for the space and time derivatives of the distribution function correspondingly. A renormalization method has been proposed to determine (alpha, beta) from the first principles (i.e. from the Hamiltonian). The anomalous transport exponent mu is derived as mu = beta/alpha or mu = beta/2 alpha for the first order mean displacement in self-similar transport.