Levy flights in comet motion and related chaotic systems

We obtain a 2-dimensional area-preserving map to study the dynamical evolut ion of comets. The presence of singularities in the energy-increment functi on leads to the Levy flight random walks for the comet energies, which resu lts in a linear increment of the energy with time. A model of stochastic dy namical system is proposed according to the map of the comet motion, which shows the existence of strong super-diffusive random walks so that the vari ance of the distributions can grow with time n as n(2m) with m greater than or equal to 1/2. (C) 2001 Elsevier Science B.V. All rights reserved.