Jacobian conjecture in $\mathbb R^2$

Xiang Zhang

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Jacobian conjecture in mathbb R²

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arxiv 2011.12701 v2 pith:7SN4BCEP submitted 2020-11-17 math.AG math.CA

Jacobian conjecture in mathbb R²

Xiang Zhang This is my paper

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keywords mathbbconjecturejacobiananswerconstantdynamicalhereinjective

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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.

Jacobian conjecture in mathbb R²

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