 
Summary: PACIFIC JOURNAL OF MATHEMATICS
Vol. 210, No. 2, 2003
EXPLOSIONS NEAR ISOLATED UNSTABLE
ATTRACTORS
Konstantin Athanassopoulos
We describe the set of explosive orbits in the region of at
traction of an unstable attractor which is isolated in the sense
of C.C. Conley. Sufficient conditions are given for the exis
tence of explosions in certain parts of the region of attraction
and for an unstable attractor to have finitely generated inte
gral AlexanderSpanier cohomology groups. Finally, we study
the case of singularities that are unstable attractors in flows
on the 2sphere.
1. Introduction.
One of the most studied parts of the phase space of a continuous flow on a
separable, locally compact, metrizable space M is the region of attraction
W of an asymptotically stable compact invariant set A, that is a Lyapunov
stable attractor. It is wellknown (see [2, Section 10], [3, Theorem V.2.9],
[8]) that there exists a strictly decreasing along the orbits in W \A uniformly
unbounded Lyapunov function f : W R+ with f1(0) = A. For any
