Poincar\'e Mechanism in Multi-scaled Hamiltonian Systems

Dynamical Systems Working Seminar
Friday, March 3, 2017 - 15:05
1 hour (actually 50 minutes)
Skiles 254
School of Mathematics, Jilin University
My talk is about the quasi-periodic motions in multi-scaled Hamiltonian systems. It consists of four part. At first, I will introduce the results in integrable Hamiltonian systems since what we focus on is nearly-integrable Hamiltonian system. The second part is the definition of  nearly-integrable Hamiltonian system and the classical KAM theorem. After then, I will introduce that  what is Poincar\'e problem and some interesting results corresponding to this problem. The last part,  which is also the main part, I will talk about the definition and the background of nearly-integrable  Hamiltonian system, then the persistence of lower dimensional tori on resonant surface, which is our recent  result. I will also simply introduce the Technical ingredients of our work.