  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.
