Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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A PERSISTENTLY SINGULAR MAP OF 𝕋n THAT IS C2 ROBUSTLY TRANSITIVE BUT IS NOT C1 ROBUSTLY TRANSITIVE

  • Received : 2020.07.10
  • Accepted : 2021.04.15
  • Published : 2021.07.01
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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

Acknowledgement

The author would like to give thanks in the first place to Dr. Jorge Iglesias without whose help this article wouldn't have been possible. And in the second place to Dr. Jorge Groisman and Dr. Roberto Markarian whose thorough reading and insightful comments helped improving the quality of this work.

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