A persistently singular map of $\mathbb{T}^n$ that is $C^2$ robustly transitive but is not $C^1$ robustly transitive

Let $\mathcal{E}$ be the set of endomorphisms of the $n$-torus. We exhibit an example of a map such 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.

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Bibliographic Details
Main Author Ramírez, Juan C. Morelli
Format Journal Article
LanguageEnglish
Published 02.04.2021
Subjects
Mathematics - Dynamical Systems
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Summary:Let $\mathcal{E}$ be the set of endomorphisms of the $n$-torus. We exhibit an example of a map such 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.
DOI:10.48550/arxiv.2104.00991