报告时间：2025年11月24日 15：00-16：00

报 告 人：刘长剑教授（中山大学）

报告地点：腾讯会议 702-756-138

报告题目：Sufficient conditions for the n-dimensional real Jacobian conjecture

内容摘要：The real Jacobian conjecture, proposed by Randall in 1983, asserts that a polynomial map F =(f1, . . . , fn) : Rn→Rn such that det DF (x)≠0 for all x∈Rn is injective. However, this conjecture is disproven by Pinchuk’s counterexample. But it is still interesting to give some sufficient conditions to be sure that the real Jacobian conjecture holds.

In this talk, firstly, we use the qualitative theory of dynamical systems to give an alternative proof of the polynomial version of the n-dimensional Hadamard’s theorem. Secondly, we present some algebraic sufficient conditions for the n-dimensional real Jacobian conjecture. Our results not only extend the main result of [J. Differential Equations 260 (2016), 5250-5258] to quasi-homogeneous type, but also generalize it from R2 to Rn. As a coproduct of our proof process, we solve an open problem formulated by Braun, Giné and Llibre in [J. Differential Equations 260 (2016), 5250-5258].

主讲人简介：刘长剑，中山大学数学注册送彩金 （珠海）副院长、教授、博士生导师，北京大学和法国里尔大学联合培养博士，主要从事常微分方程定性理论的研究工作，已主持多项国家自然科学基金面上项目，在Trans. Amer. Math. Soc.、Nonlinearity、J. Diff. Equa.、Dis. Cont. Dyn. Sys.等高水平杂志上发表多篇学术论文。