The Departments of

Mathematical Sciences

and

Mechanical Engineering

Presents

Prof. Huachu Qin

Institute of Systems Science

Chinese Academy of Science

Beijing, P.R. China

Friday, March 7, 2003

2:30-3:20 p.m. CBC C-118

Topic

“Results on Jacobian Conjecture about Globally Asymptotic Stability”

Abstract

There are two topics concerning Jacobian Conjecture in mathematical literature. One is about stability of differential equations as presented in this talk. Another one is about the injectivity of polynomial mappings which is still an open problem.

Let . The Jacobian Conjecture states that if for any , the eigenvalues of the Jacobian matrix have negative real parts, then the zero solution of the differential equation is globally asymptotically stable. I will briefly present the following topics concerning the Jacobian Conjecture:

1. The history of studying Jacobian Conjecture and the result of Jacobian Conjecture.

2. The result about Jacobian Conjecture on bounded and closed region from the viewpoint of practical applications.

3. Present an estimate approach of attraction region for planary nonlinear differential equation system.

College of Sciences

The University of Nevada, Las Vegas