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On the concept of attractor: correction and remarks. (English) Zbl 0602.58030

The author makes a correction and adds several remarks to his paper mentioned in the title [ibid. 99, 177-195 (1985; Zbl 0595.58028)]. He shows that ”stability” of the attractor implies ”asymptotic stability”, where by stability we mean that for any sufficiently small neighborhood U of the attractor A, the intersection of the forward images \(f^ n(A)\) is precisely A.
Reviewer: R.Devaney

MSC:

37C70 Attractors and repellers of smooth dynamical systems and their topological structure
37C75 Stability theory for smooth dynamical systems
26A18 Iteration of real functions in one variable
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