CONVERGENCE TO TRAP ALMOST EVERYWHERE FOR FLOWS GENERATED BY COOPERATIVE AND IRREDUCIBLE VECTOR-FIELDS

This paper is concerned with the asymptotic behavior of cooperative sy stems in W subset-of R(n). For a C2 cooperative system whose Jacobian matrices are irreducible, it is proved that the forward orbit converge s to an equilibrium for almost every point having compact forward orbi t closure and the set of all points which have compact forward orbit c losure's and do not converge to a semi-asymptotically stable equilibri um is meager in W if the equilibrium set cannot contain a simply order ed curve. The invariant function and the geometry of the stable manifo ld of an unstable equilibrium are considered.