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

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

18 Citations (Scopus)

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.

Original language	English
Pages (from-to)	1187-1201
Journal	Canadian Journal of Mathematics
Volume	54
Issue number	6
DOIs	https://doi.org/10.4153/CJM-2002-045-0
Publication status	Published - 1 Jan 2002

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title = "On the injectivity of C 1 maps of the real plane",

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.",

author = "Milton Cobo and Carlos Gutierrez and Jaume Llibre",

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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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JF - Canadian Journal of Mathematics

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