a) Let X : R 2 -R 2 be a differentiable map (not necessarily C 1 ) and let SpecðX Þ be the set of (complex) eigenvalues of the derivative DX p when p varies in R 2 : If, for some e40; SpecðX Þ-½0; eÞ ¼ | then X is injective.(b) Let X : R 2 -R 2 be a differentiable vector field such that X ð0Þ ¼ 0 and SpecðX ÞCfzAC : RðzÞo0g: Then, for all pAR 2 ; there is a unique positive trajectory starting at p; moreover the o-limit set of p is equal to f0g: r 2004 Elsevier Inc. All rights reserved.

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