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It is demonstrated that a C^1-unipotent map is globally equivalent to thelinear translation T(x,y)=(x+1,y), if the map is fixed point free Similarly, itis proved not only that the fixed point set induced by a C^1-unipotent has noisolated elements, but that a $C^1-$unipotent map has no periodic points. Therelation with the existence of global attractors in R^2, by using a globalbifurcation on unipotent maps, is also studied.

An spectral condition for global equivalence of planar maps