Mathematical Sciences: Ordered and Chaotic Motions in Hamiltonian Systems

本课题致力于研究近可积无限维哈密顿系统中的规则运动和混沌运动。这类系统包括某些非线性偏微分方程，例如波动梁方程和振动梁方程。统计力学和凝聚态物理也导致这些系统。该方法将KAM理论推广到完全可积哈密顿系统的摄动。与常用的变分演算和分岔分析方法一起，KAM理论将对周期解和准周期解的存在性提供新的解释。此外，几何和数值方法将被采用。

This project is devoted to the study of regular and chaotic motion in nearly integrable infinite dimensional hamiltonian systems. Such systems include certain nonlinear partial differential equations, the wave and vibrating beam equations for instance. Statistical mechanics and condensed matter physics also lead to these systems. The approach consists of extending KAM theory to perturbations of completely integrable hamiltonian systems. Together with the usual methods of the calculus of variation and bifurcation analysis, KAM theory will shed new light on the existence of periodic and quasiperiodic solutions. In addition, geometric and numerical methods will be employed.