Roughly speaking, an attractor is an invariant set which
attracts everything in a neighborhood of itself. Attractors persist in
the sense that, given a system with an attractor, every nearby system has
a corresponding attractor. As before, one can ask how big a perturbation
is allowed.
As described in detail , the answer is intimately
tied to the strength by which the attractor attracts. Strong attractors
persist further than weak attractors. An attractor will persist for
all systems
within a distance, in the
metric, given by the
intensity of attraction.
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Copyright (c) 1998 by Richard
McGehee, all rights reserved.
Last modified: July 31, 1998.