An spectral condition for global equivalence of planar maps

Abstract

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

To appear in Journal of Difference Equations and Applications

References in corpus (1)

• The theorem of Kerekjarto on periodic homeomorphisms of the disc and the sphere