Geodesic
On the Injectivity of C 1 Maps of the Real Plane
Canadian journal of mathematics, Tome 54 (2002) no. 6, pp. 1187-1201

Voir la notice de l'article provenant de la source Cambridge University Press

Let $X:\,{{\mathbb{R}}^{2}}\to \,{{\mathbb{R}}^{2}}$ be a ${{C}^{1}}$ map. Denote by $\text{Spec}(X)$ the set of (complex) eigenvalues of $\text{D}{{\text{X}}_{p}}$ when $p$ varies in ${{\mathbb{R}}^{2}}$ . If there exists $\in \,>\,0$ such that $\text{Spec(}X)\,\bigcap \,(-\in ,\,\in )\,=\,\varnothing $ , then $X$ is injective. Some applications of this result to the real Keller Jacobian conjecture are discussed.
DOI : 10.4153/CJM-2002-045-0
Mots-clés : 34D05, 54H20, 58F10, 58F21 
Cobo, Milton; Gutierrez, Carlos; Llibre, Jaume. On the Injectivity of C 1 Maps of the Real Plane. Canadian journal of mathematics, Tome 54 (2002) no. 6, pp. 1187-1201. doi: 10.4153/CJM-2002-045-0
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