近可积Hamilton系统动力学的多样性

Dynamical diversity of nearly integrable Hamiltonian systems

近可积Hamilton系统的研究被Poincaré称为动力学的基本问题.自20世纪中叶以来,相关研究取得了巨大进展.Kolmogorov定理的建立和Arnold扩散现象的发现是其中的两大里程碑,极大地深化了我们对于近可积Hamilton系统动力学多样性的理解.本文将就相关内容作简要介绍.

The dynamics of nearly integrable Hamiltonian is called by Poincar′e the fundamental problem of dynamical systems.Since the fifties of the last century,the great achievements have been made in the study of the problem.Among them,the Kolmogorov’s theorem on invariant tori and the discovery of Arnold diffusion are the landmarks.They have greatly deepened our understanding on the dynamical diversity of nearly integrable Hamiltonian systems.We shall briefly review some of the developments.