An exotic Denjoy example of class $C^1$

Maximiliano Escayola

An exotic Denjoy example of class $C^1$

Dynamical Systems 2026-07-13 v1

Authors: Maximiliano Escayola

Abstract

We construct a $C^1$ -diffeomorphism of the circle having an invariant Cantor minimal set such that, when the lengths of the connected components of its complement are arranged in decreasing order, the ratios of consecutive lengths do not converge to 1. This gives a negative answer to a longstanding question posed by Dusa McDuff.

Keywords

Denjoy example C^1 diffeomorphism Cantor minimal set circle dynamics McDuff question

Cite

@article{arxiv.2607.11616,
  title  = {An exotic Denjoy example of class $C^1$},
  author = {Maximiliano Escayola},
  journal= {arXiv preprint arXiv:2607.11616},
  year   = {2026}
}