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Connected components of attractors and other stable sets
Abstract
Let f be a continuous map on a locally connected metric space. If A is an attractor in the sense of C. Conley then f permutes its components, and if A is indecomposable the permutation is cyclic. If Y is an indecomposable stable invariant set with infinitely many components, the action of f on them is a generalized adding machine, and it has no periocic orbits in Y.
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