Ii. Shevchenko et H. Scholl, INTERMITTENT TRAJECTORIES IN THE 3 1 JOVIAN RESONANCE/, Celestial mechanics & dynamical astronomy, 68(2), 1997, pp. 163-175
The statistical behaviour of intermittent trajectories at the 3/1 reso
nance is investigated. The elliptic planar restricted three-body probl
em is used as a model. Distribution functions for time intervals D bet
ween eccentricity bursts are obtained and theoretically interpreted. F
or smaller values of D, the distribution is found to be of Poisson typ
e, while in its tail it is described by a power law D-alpha. This chan
ge in the distribution occurs for values of D in the range 10(5)-10(6)
Jupiter periods. The power-law index alpha for the integral distribut
ions lies in the range (-2, -1) and is trajectory dependent. The algeb
raic decay in the tails of the distributions is explained by the pheno
menon of sticking of orbits to the chaos border during long intervals
between bursts.