Anomalous diffusion in the first-order Jovian resonance
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
, where σ is the standard deviation and
. 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