EDP Sciences
Free access
Volume 439, Number 1, August III 2005
Page(s) 375 - 385
Section Celestial mechanics and astrometry
DOI http://dx.doi.org/10.1051/0004-6361:20052798

A&A 439, 375-385 (2005)
DOI: 10.1051/0004-6361:20052798

Anomalous diffusion in the first-order Jovian resonance

R. R. Cordeiro1 and L. A. Mendes de Souza2

1  Departamento de Física, Universidade Federal de Viçosa, Viçosa - MG, 36571-000, Brazil
    e-mail: cordeiro@ufv.br
2  Departamento de Física, Universidade Federal de Minas Gerais, Belo Horizonte - MG, 31270-901, Brazil

(Received 31 January 2005 / Accepted 12 April 2005)

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 $\sigma\propto t^H$, where $\sigma$ is the standard deviation and $\frac{1}{2}<H<1.7$. The values of exponent H were determined in grids of initial conditions in the 2:1, 3:2 and 4:3 Jovian resonances.

Key words: diffusion -- minor planets asteroids

© ESO 2005