Bifurcations and Homo- and Heteroclinic Behavior in Infinite- Dimensional Dynamical Systems

点击翻译按钮获取中文摘要

Bifurcations and homo- and heteroclinic motions in several infinite-dimensional dynamical systems such as partial differential equations and discrete lattices were studied. In particular, perturbation methods to obtain conditions for saddle-node and pitchfork bifurcations of homo- and heteroclinic orbits in ordinary differential equations, which correspond to soliton, pulse and front solutions in partial differential equations, were developed, and their relationship with the integrability of variational equations around these orbits in the meaning of differential Galois theory was