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PACIFIC JOURNAL OF MATHEMATICS Vol. 210, No. 2, 2003
 

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 Alexander-Spanier cohomology groups. Finally, we study
the case of singularities that are unstable attractors in flows
on the 2-sphere.
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 well-known (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 f-1(0) = A. For any

  

Source: Athanassopoulos, Konstantin - Department of Mathematics, University of Crete

 

Collections: Mathematics