动力系统与微分方程系列学术报告（十二）：Jacobian conjecture in $\mathbb R^2$

讲座时间 Datetime: 

星期二, 2020/12/22 - 从 16:30 到 19:30

地点 Venue: 

腾讯会议114 611 948

报告人 Speaker: 

张祥 教授

单位 Affiliation: 

上海交通大学

报告摘要 Abstract: 

Jacobian conjecture was first posed by Keller in 1939, and was listed by Smale in 1998 as his 16th problems of 18 problems. This conjecture states that if $F:\ \mathbb C^n~(\mathbb R^n) \rightarrow \mathbb C^n~(\mathbb R^n)$ is a polynomial map such that the Jacobian of $F$ is a nonzero constant, then $F$ is injective. This conjecture is still open for all $n\ge 2$, and for both $\mathbb C^n$ and $\mathbb R^n$. Here we provide a positive answer to the Jacobian conjecture in $\mathbb R^2$ via the tools from the theory of dynamical systems.