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arXiv · 1512.03171

Indestructible dynamics of torus maps

Suddhasattwa Das·James Yorke
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Abstract

Given a $d$-dimensional torus map $F(z)=Mz+G(z)\bmod 1$, where $M$ is an integer-matrix and and $G$ is a periodic function, we find conditions on $M$ under which $F$ is semi-conjugate to a linear torus map, independently of $G$. We also find a conditions $G$ under which these semi-conjugacies can be turned into conjugacies. These conditions are satisfied by open sets of torus maps (in the $C^1$-topology) and therefore describe some asymptotic behavior of trajectories which are stable under perturbations to the map.

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Suddhasattwa Das, James Yorke. 2016-04-08. Indestructible dynamics of torus maps. https://doi.org/10.1137/17m1113199

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