Abstract:The ideas of renormalization was introduced into dynamics around 40 years ago. By now renormalization is one of the most powerful tools in the asymptotic analysis of dynamical systems. In this talk I will discuss the main conceptual features of the renormalization approach,and present a selection of recent results. I will also discuss open problems and formulate related conjectures.Sp...
Record: YesLevel: GraduateLanguage: ChinesePrerequisiteAbstractThis course is a continuation of last semester and will cover the following topics:1) Normal forms of Hamiltonian systems and bifurcation theory;2) Averaging methods of classical perturbation theory;3) KAM stability of Hamiltonian systems;4) Effective stability of nearly integrable systems;5) Numerical stability of symplectic g...