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Several endomorphisms of the plane have been constructed by simple maps. We study the dynamics occuring in one of them, which is rich in global bifurcations. The invariants sets are stable manifolds of saddle type points or cycles, as well as closed curves issued from Hopf bifurcations. The present paper focuses some bifurcations related with attractors or basins which produce other attractors which coexist with invariant sets.
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