Costa, Fernando Pestana da2010-07-152010-07-152007Costa, Fernando Pestana da - Dynamics of a differential system using invariant regions. "L'Enseignement Mathematique" [Em linha]. ISSN 0425-0818. Vol. 53, nº 2 (2007), p. 3-140425-0818http://hdl.handle.net/10400.2/1533The longtime behaviour of a two dimensional system of ordinary differential equations with singularities is studied using conveniently defined positively invariant sets and auxiliary functions. The approach uses only elementary techniques of phase plane analysis and provides a good geometric insight into the dynamical behaviour of the system. It provides dynamical information analogous to what is usually obtained via centre manifold techniques but does not require the flow to be defined at the limit point.engOrdinary diferential equationsAsymptotic behaviour of solutionsInvariant regionspreprint