A family of quadratic maps of the plane has been found numerically for certain parameter values to have three attractors, in a triangular pattern, with ``intermingled'' basins. This means that for every open set $S$, if the basin of attraction of one of the attractors intersects $S$ in a set of positive Lebesgue measure, then so do the other two basins. In this paper we mathematically verify this observation for a particular parameter, and prove that our results hold for a set of parameters with positive Lebesgue measure.Click here for a PostScript copy (650K) of this paper. The file omits page 5, which consists of a color picture (Figure 2). Click here for a GIF copy (100K) of this picture.
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