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。