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 | |
| 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