Intermingled basins for the triangle map
1996
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.
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