Geometric objects in Hamiltonian systems with weak dissipation and weak forcing
报告题目(Title)：Geometric objects in Hamiltonian systems with weak dissipation and weak forcing
报告人(Speaker)：Rafael de la Llave 教授（Georgia Institute of Technology）
地点(Place)：Zoom会议：636 918 43731 密码：123456
时间(Time)：12月22日 09：30 —10：30
邀请人(Inviter)：苏喜锋
报告摘要
Many practical systems (e.g. in celestial mechanics, mechanical engineering) can be described as hamiltonian systems modified by small friction. Even adding a small friction changes the very long term behavior very drastically, many features of the motion can be analyzed.
I will describe two recent works:
If the Hamiltonian system has a KAM torus, it is possible to
obtain asymptotic expansions in the friction of the needed forcing so that the perturbed system has a quasi-periodic solution of the same frequency. These series do not converge, but indeed, there is a quasi periodic solution with a complicated domain of analyticity. We study these series and show that they are Gevery. (Joint work with A. Perez Bustamante)
If the Hamiltonian systems has separatrices (orbits for which the stable and unstable manifolds agree). A general perturbation may lead to transverse homoclinic intersections. We describe generalizations of the classical Melnikov method to dissipative perturbations. (Joint work with M. Gidea and M. Musser).
主讲人简介
Rafael de la Llave，佐治亚理工大学教授，2006年国际数学家大会邀请报告人。
