Academic Report
Title: A KAM-Theorem for Invariant Tori in Bifurcations of Equilibrium Points
Reporter:LI Xuemei (Hunan Normal University)
Time: April 20, 2018(Friday) PM 15:00-16:00
Location: A#1101 room, Innovation Park Building
Contact: A.Prof. CONG Hongzi(tel: 84708351-8137)
Abstract: In this talk, we focus on the persistence of invariant tori in bifurcations of equilibrium points. We establish a KAM-theorem for ordinary differential equations of finitely differentiable vector fields with multiple degeneracies. The theorem can be used to deal with the persistence of quasi-periodic invariant tori in multiple Hopf bifurcations and zero-multiple Hopf bifurcations, as well as their subordinate bifurcations, of equilibrium points of continuous dynamical systems, such as ordinary differential equations, delay differential equations etc.
The brief introduction to the reporter: Li Xuemei is the professor and doctoral supervisor of the institute of mathematics and statistics, Hunan Normal University. The main research fields involve the existence and regularity of quasi-periodic solutions (invariant torus) of ordinary differential equations and delay differential equations and the dynamical properties of artificial neural nets.She has published more than 40 papers in JDE, IEEE-TCAS and Neural Comp and other publications, and has hosted and completed 3 projects on the National Natural Science Foundation. S he obtained her master's degree in basic mathematics from Inner Mongolia University in 1987 and obtained her Ph.D. in Applied Mathematics from Hunan University. Then she worked at Hunan Normal University in 1987. And she was Invited many times to visit the Academy of mathematics and Systems Sciences of the Chinese Academy of Sciences, Fudan University, the University of Texas at Austin, the CRM Institute in Spain and so on.
