天体运动中的轨道扩散现象

In this project, we study the influence of orbital diffusion to the dynamical stability of comets and asteroids, and extend the diffusion laws to Hamiltonian dynamics. The main results are: partly.explain the long-term existence of Uranian epsilon rings from the dynamical point of view, find that the energy evolution of the long-periodic comets obeys the Levy flight random walk, and stochastic factors such as scattering between celestial bodies can affect the dynamical evolution.and distribution of asteroid in the Kuiper Belt. We obtain a criterion for the critical parameters when the 3-dimensional invariant tori breaks in a Hamiltonian System with three degrees of freedom, and with this criterion the universal critical distribution is found. We prove rigorously.the existence of chaotic motion and Poincare Recurrence in a mixing measure-preserving transformation. We also made some preliminary study on the interaction between discs and pro-planets in extra planet systems. We have published 15 papers in international journals,.includes 11 SCI journals. One of the works is reported in the 2000 workshop of Celestial Mechanics held in Poland. 1 conference paper is published.

轨道扩散现象对太阳系小天体、密近双星系统吸积盘等的形成与长期动力演化有重要影响。本项目拟采用天体力学的映射方法来研究太阳系彗星、小行星以及密近双星系统吸积盘的形成和演化中的轨道扩散问题，在解决实际天文问题、发现新现象的同时，对轨道扩散路径等一般哈密顿系统轨道扩散方面的数学问题作一些理论研究。