Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

Article

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J. Korean Math. Soc. 2021; 58(4): 977-1000

Published online July 1, 2021 https://doi.org/10.4134/JKMS.j200403

Copyright © The Korean Mathematical Society.

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

Juan Carlos Morelli

Universidad de la Rep\'ublica

Abstract

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.