Abstract

We describe the set of explosive orbits in the region of attraction of an unstable attractor which is isolated in the sense of C.C. Conley. Suficient conditions are given for the existence of explosions in certain parts of the region of attraction and for an unstable attractor to have finitely generated integral Alexander-Spanier cohomology groups. Finally, we study the case of singularities that are unstable attractors in flows on the 2-sphere.

Authors