On the injectivity of C 1 maps of the real plane

Milton Cobo; Carlos Gutierrez; Jaume Llibre

doi:10.4153/CJM-2002-045-0

On the injectivity of C ¹ maps of the real plane

Milton Cobo, Carlos Gutierrez, Jaume Llibre

Departament de Matemàtiques

Producció científica: Contribució a revista › Article › Recerca › Avaluat per experts

26 Cites (Scopus)

Resum

Let X : ℝ 2 → ℝ 2 be a C 1 map. Denote by Spec(X) the set of (complex) eigenvalues of DX p when p varies in ℝ 2 . If there exists ε > 0 such that Spec(X) ∩ (-ε, ε) = ∅, then X is injective. Some applications of this result to the real Keller Jacobian conjecture are discussed.

Idioma original	Anglès
Pàgines (de-a)	1187-1201
Revista	Canadian Journal of Mathematics
Volum	54
Número	6
DOIs	https://doi.org/10.4153/CJM-2002-045-0
Estat de la publicació	Publicada - 1 de gen. 2002

Accés al document

10.4153/CJM-2002-045-0

Altres arxius i enllaços

https://www.scopus.com/pages/publications/0036972513

Com citar-ho

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abstract = "Let X : ℝ 2 → ℝ 2 be a C 1 map. Denote by Spec(X) the set of (complex) eigenvalues of DX p when p varies in ℝ 2 . If there exists ε > 0 such that Spec(X) ∩ (-ε, ε) = ∅, then X is injective. Some applications of this result to the real Keller Jacobian conjecture are discussed.",

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AB - Let X : ℝ 2 → ℝ 2 be a C 1 map. Denote by Spec(X) the set of (complex) eigenvalues of DX p when p varies in ℝ 2 . If there exists ε > 0 such that Spec(X) ∩ (-ε, ε) = ∅, then X is injective. Some applications of this result to the real Keller Jacobian conjecture are discussed.

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