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Basins of Wada. (English) Zbl 0746.58054
The authors describe situations where there are several regions with the Wada property, namely that each point that is on the boundary of one region is on the boundary of all. First, the classical example of the “Lakes of Wada” is discussed. Then it is argued by numerical computations (and proved for a somewhat idealized situation) that for the forced damped pendulum three attractor regions (of attracting periodic orbits) may coexist and all three basins of attraction have the Wada property. The latter requires some kind of indecomposability of the sets. Indecomposable continua are discussed in the rest of the paper.
Reviewer: G.Jetschke (Jena)

MSC:
37C70 Attractors and repellers of smooth dynamical systems and their topological structure
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
34C25 Periodic solutions to ordinary differential equations
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