Mathematical Sciences: Ordered and Chaotic Motions in Hamiltonian Systems

本项目致力于研究几乎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组，例如波动和振动梁方程。统计力学和凝聚态物理也导致了这些系统的产生。该方法包括将KAM理论推广到完全可积的哈密顿系统的摄动。结合变分和分叉分析的常用方法，KAM理论将为周期解和拟周期解的存在性提供新的线索。此外，还将采用几何和数值方法。

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.