Abstract
A very simple two-dimensional map is discussed. It is shown that forappropriate values of the parameters there is a two-dimensional subset ofthe plane on which the dynamics is transitive and periodic orbits aredense, but that this topological attractor contains a one-dimensional setwhich attracts almost all points(i.e. it is a Milnor attractor). This arises naturally as a precursor to ablowout bifurcation to on-off intermittency in this system, and confirmsa conjecture due to Pikovsky and Grassberger.
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