Mathematical Sciences: Ordered and Chaotic Motions in Hamiltonian Systems

本项目致力于研究规则和混沌 近可积无穷维哈密顿量中的运动 系统. 这样的系统包括某些非线性部分 微分方程，波动和振动梁方程， instance. 统计力学与凝聚态物理 也导致了这些系统。 该方法包括扩展KAM理论， 完全可积Hamilton系统的扰动 结合变分法的常用方法， 分叉分析，KAM理论将揭示新的光 周期解和拟周期解的存在性。 此外，本发明还提供了一种方法， 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.