Period sets of linear toral endomorphisms on T²

2014/06/20 by Llibre, Jaume, Neumärker, Natascha
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1406.5332

Abstract

The period set of a dynamical system is defined as the subset of all integers n such that the system has a periodic orbit of length n. Based on known results on the intersection of period sets of torus maps within a homotopy class, we give a complete classification of the period sets of (not necessarily invertible) toral endomorphisms on the 2--dimensional torus \mathbbT².

Related

• The rotation set and periodic points for torus homeomorphisms
• On torus homeomorphisms whose rotation set is an interval
• Volumes of end-periodic mapping tori
• Orbits of certain endomorphisms of nilmanifolds and Hausdorff dimension
• Uniformly distributed periodic orbits of endomorphisms on n-tori