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Let X:R²→R² be a differentiable map (not necessarily C¹), and let Spec(X) denote the set of real or complex eigenvalues of its Jacobian matrix DX_p when p varies in R². Then
(i) If, for some ε>0, Spec(X)∩[0,ε)=∅, then X is injective.
(ii) If X(0)=0 and Spec(X)⊂{z∈C:Re(z)<0}, then for any p∈R² the Cauchy problem x’=X(x), x(0)=p, has a unique positive trajectory and its ω-limit set is {0}.

Autor(es):
Fernándes, Alexandre; Gutierrez, Carlos; Rabanal, Roland
Año: 2004
Título de la revista: Journal of Differential Equations
Volumen: Volume 206
Número: 10
Página inicial - Página final: 470–482
ISSN: 0022-0396
Url: https://www.sciencedirect.com/science/article/pii/S0022039604001822