Anomalous diffusion in the asteroid belt

摘要

This paper presents a new method for the analysis of "diffusion'' in Hamiltonian systems, especially in regard to orbital problems. Although the new method resembles another one developed in an earlier paper, it introduces new concepts related to the "diffusive processes'' observed in some dynamical systems. As a consequence, it is a substantial improvement, capable of more thoroughly explaining details observed in standard deviation time series of physical parameters. In the current study the new method is described, briefly applied to some Hamiltonian systems, and more methodically employed to analyze diffusive processes in the Jovian 2:1 mean-motion resonance and in the orbital behavior of stable asteroids with large Lyapunov characteristic exponents. A global view of diffusive processes in semimajor axis and eccentricity for test particles in the asteroid belt is then presented in the form of histograms, followed by a comparison of the study's results with the actual distribution of small bodies in the asteroid belt.