Anomalous diffusion in the first-order Jovian resonance

A method is presented for the characterization of anomalous diffusive processes in dynamical systems. This method is applied to the analysis of the diffusion in some Hamiltonian systems with special emphasis on the orbital problems. We show that the types of diffusion processes in the borders and in the resonant regions are common for all the studied systems. In the borders the diffusion is governed by an initial exponential stage and in the resonant regions the diffusion is also represented by a power law. In the orbital problem we show that, in general, the resonant asteroids are associated with regions where diffusive processes for the semi-major axis and eccentricity are described by sigma proportional to t(H), where sigma is the standard deviation and 1/2 < H < 1.7. The values of exponent H were determined in grids of initial conditions in the 2:1, 3:2 and 4:3 Jovian resonances.