Basins of Wada (Q1181169)

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.