Recent advances on linearization of differential equations
Speaker:Prof. Yonghui Xia
Professor of Department of Mathematics, Zhejiang Normal University
Date & Time:19 Jan 2015 (Monday) 10:30 - 11:30
Venue:E11-1009
Organized by:Department of Mathematics

Abstract

A fundamental contribution to the linearization problem for autonomous differential equations is the famous Hartman-Grobman theorem. In 1973, Palmer successfully generalized Hartman's linearization theorem to non-autonomous cases under the assumption that the linear system possesses an exponential dichotomy and nonlinear term is bounded. This talk reports the recent advances on the generalized Hartman-Grobman type linearization theorem. We extended the classical linearization theorem to more general cases. On one hand, we extended the nonlinear term to unbounded cases. On the other hand, we generalized the Hartman-Grobman theorem to dynamic equations on measure chain or time scales.

Biography

Prof. Xia currently is professor in Department of Mathematics at Zhejiang Normal University. He obtained his PhD degree at The Institute of Mathematics at Shanghai Normal University in 2009. His research experience in differential equations include nonlinear systems, mathematical biology, neural networks, bifurcations and stability analysis in dynamic systems (including continuous, discrete and impulsive systems),bifurcations of delayed differential equations including mathematical biology and neural networks。His present research focuses on the study of linearization of differential equations and spectrum of exponential dichotomy. He is the author of more than 30 journal papers such as Journal of Differential Equations, SIAM Journal on Applied Mathematics, IEEE Transaction on Neural Network, Proceedings of Edinburgh Mathematical Society, Journal of Mathematical Analysis and Applications, etc.