### 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 |
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Pages (from-to) | 1187-1201 |

Journal | Canadian Journal of Mathematics |

Volume | 54 |

Issue number | 6 |

DOIs | |

Publication status | Published - 1 Jan 2002 |

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## Cite this

Cobo, M., Gutierrez, C., & Llibre, J. (2002). On the injectivity of C

^{1}maps of the real plane.*Canadian Journal of Mathematics*,*54*(6), 1187-1201. https://doi.org/10.4153/CJM-2002-045-0