An spectral condition for global equivalence of planar maps
Abstract
It is demonstrated that a C1-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 C1-unipotent has no isolated elements, but that a C1-unipotent map has no periodic points. The relation with the existence of global attractors in R2, by using a global bifurcation on unipotent maps, is also studied.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.