J. Korean Math. Soc. 2021; 58(4): 977-1000
Online first article June 1, 2021 Printed July 1, 2021
https://doi.org/10.4134/JKMS.j200403
Copyright © The Korean Mathematical Society.
Juan Carlos Morelli
Universidad de la Rep\'ublica
Consider the high dimensional torus $\mathbb{T}^n$ and the set $\mathcal{E}$ of its endomorphisms. We construct a map in $\mathcal{E}$ that is robustly transitive if $\mathcal{E}$ is endowed with the $C^2$ topology but is not robustly transitive if $\mathcal{E}$ is endowed with the $C^1$ topology.
Keywords: Transitivity, singularities, stability, high dimension
MSC numbers: Primary 37C20; Secondary 57R45, 57N16
Supported by: This work was partially financed by ANII of Uruguay.
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