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arXiv · 1406.5332

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

Jaume Llibre·Natascha Neumärker
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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 $\mathbb{T}^2$.

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Jaume Llibre, Natascha Neumärker. 2014-06-20. Period sets of linear toral endomorphisms on $T^2$. https://arxiv.org/abs/1406.5332

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