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http://dx.doi.org/10.4134/JKMS.j200403

A PERSISTENTLY SINGULAR MAP OF 𝕋n THAT IS C2 ROBUSTLY TRANSITIVE BUT IS NOT C1 ROBUSTLY TRANSITIVE  

Morelli, Juan Carlos (Facultad de Ingenieria Universidad de la Republica)
Publication Information
Journal of the Korean Mathematical Society / v.58, no.4, 2021 , pp. 977-1000 More about this Journal
Abstract
Consider the high dimensional torus 𝕋n and the set 𝜺 of its endomorphisms. We construct a map in 𝜺 that is robustly transitive if 𝜺 is endowed with the C2 topology but is not robustly transitive if 𝜺 is endowed with the C1 topology.
Keywords
Transitivity; singularities; stability; high dimension;
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