Period sets of linear toral endomorphisms on $T^2$

Jaume Llibre; Natascha Neumärker

Period sets of linear toral endomorphisms on $T^2$

Dynamical Systems 2014-06-23 v1

Authors: Jaume Llibre , Natascha Neumärker

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 $\mathbb{T}^2$ .

Keywords

period set toral endomorphisms dynamical systems periodic orbits homotopy class classification $\mathbb{T}^2$

Cite

@article{arxiv.1406.5332,
  title  = {Period sets of linear toral endomorphisms on $T^2$},
  author = {Jaume Llibre and Natascha Neumärker},
  journal= {arXiv preprint arXiv:1406.5332},
  year   = {2014}
}

Comments

10 pages

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