An spectral condition for global equivalence of planar maps

TL;DR

This paper establishes a spectral condition under which planar C^1-unipotent maps are globally equivalent to a linear translation, exploring fixed point properties and implications for global attractors.

Contribution

It introduces a spectral condition that guarantees global equivalence of planar unipotent maps to a translation, and analyzes fixed point and attractor properties.

Findings

C^1-unipotent maps fixed point free are globally equivalent to translation

Such maps have no isolated fixed points or periodic points

Connection to global attractors in R^2 is studied

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.