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arXiv · 2011.12701

Jacobian conjecture in $\mathbb R^2$

Xiang Zhang
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Abstract

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.

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Xiang Zhang. 2020-11-17. Jacobian conjecture in $\mathbb R^2$. https://arxiv.org/abs/2011.12701

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