题目：The necessary and sufficient conditions for the real Jacobian conjecture

时间：2021年9月10日 星期五下午：15：30——16：30

摘要：In this talk, we focus on investigating the real Jacobian conjecture. The talk consists of two parts. The first part is to study  the two-dimensional real Jacobian conjecture via the method of the qualitative theory of dynamical systems. We provide some necessary and sufficient conditions such that the two-dimensional real Jacobian conjecture holds. Applying these results we present an algebraic criterion such that two-dimensional real Jacobian conjecture holds.  This algebraic criterion improves the main result of Braun et al [JDE 260(2016) 5250-5258]. In the second part, the necessary and sufficient conditions on the n-dimensional real Jacobian conjecture is obtained. Using the tool from the nonlinear functional analysis, F(x)  is a global injective if and only if the norm of F(x) approaches to infinite as the norm of x tends to infinity, which is a generalization of  the   algebraic criterion of  two-dimensional.

报告人简介：赵育林，中山大学数学学院（珠海）院长、博士生导师， 2007入选教育部新世纪优秀人才支持计划。赵育林教授从事常微分方程定性理论和分支理论的研究工作，包括弱化的Hilbert 十六问题、周期单调性、代数极限环、高阶极限环分支问题等，已在J. Differential Equation、Nonlinearity、中国科学（英文版）等期刊上发表多篇学术论文。