New sufficient condition for the two-dimensional real Jacobian conjecture through the Newton diagram

讲座时间 Datetime: 2022年5月21日，星期六，16:30-17:30

地点 Venue: 腾讯线上会议：370-526-311

 主持人 Host：刘长剑

报告人 Speaker:岑秀丽

单位 Affiliation:中南大学

报告摘要 Abstract:

The present paper is devoted to investigating the two-dimensional real Jacobian conjecture. This conjecture claims that if $F=\left(f,g\right):\mathbb{R}^2\rightarrow \mathbb{R}^2$ is a polynomial map with $\det DF\left(x,y\right)\ne0$ for all  $\left(x,y\right)\in\mathbb{R}^2$, then $F$ is globally injective.  With the help of the Newton diagram, we provide a new sufficient condition such that the two-dimensional real Jacobian conjecture holds.  Moreover, this sufficient condition generalizes the main result of [J. Differential Equations {\bf 260} (2016), 5250-5258]. Some examples are given to  illustrate our main results.