Density of the set of attractive compacta

A compact set $K$ in a smooth closed manifold $M$ is said to be attractive, if on $M$ there exists a system of differential equations, for which $K$ is an asymptotically stable invariant set. It is proved that the set of attractive compacta is dense and its complement contains a dense set of type $G_\delta$ in the space of all compacta of the manifold $M$ endowed with two natural topologies.