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On the Injectivity of $C^1$ Maps of the Real Plane

Open Access article
 Printed: Dec 2002
  • Milton Cobo
  • Carlos Gutierrez
  • Jaume Llibre
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Let $X\colon\mathbb{R}^2\to\mathbb{R}^2$ be a $C^1$ map. Denote by $\Spec(X)$ the set of (complex) eigenvalues of $\DX_p$ when $p$ varies in $\mathbb{R}^2$. If there exists $\epsilon >0$ such that $\Spec(X)\cap(-\epsilon,\epsilon)=\emptyset$, then $X$ is injective. Some applications of this result to the real Keller Jacobian conjecture are discussed.
MSC Classifications: 34D05, 54H20, 58F10, 58F21 show english descriptions Asymptotic properties
Topological dynamics [See also 28Dxx, 37Bxx]
unknown classification 58F10
unknown classification 58F21
34D05 - Asymptotic properties
54H20 - Topological dynamics [See also 28Dxx, 37Bxx]
58F10 - unknown classification 58F10
58F21 - unknown classification 58F21

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