论文标题
Jacobian猜想$ \ Mathbb r^2 $
Jacobian conjecture in $\mathbb R^2$
论文作者
论文摘要
Jacobian的猜想指出，如果$ f：\ \ mathbb c^n（\ mathbb r^n）\ rightArrow \ rightarrow \ mathbb c^n（\ mathbb r^n）$是一张多项式图，使得$ f $的jacobian of $ f $ of $ f $是非零的常数，那么$ f $ and $ f $ in Dimentive in Imentive in Imentive。此猜想仍然针对所有$ n \ ge 2 $打开，并且均为$ \ Mathbb c^n $和$ \ Mathbb r^n $。在这里，我们通过动态系统理论的工具对$ \ Mathbb r^2 $中的Jacobian猜想提供了积极的答案。
Jacobian 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.
