Denjoy examples of class $C^1$ with affine dynamics outside the invariant Cantor set

Victor Kleptsyn; Andrés Navas

Denjoy examples of class $C^1$ with affine dynamics outside the invariant Cantor set

Dynamical Systems 2026-07-13 v1

Authors: Victor Kleptsyn , Andrés Navas

Abstract

Given any irrational number, we construct a Denjoy example of class $C^1$ with this rotation number, that is exactly affine on each interval of the complement to the exceptional minimal set.

Keywords

Denjoy examples rotation number affine dynamics invariant Cantor set exceptional minimal set

Cite

@article{arxiv.2607.11748,
  title  = {Denjoy examples of class $C^1$ with affine dynamics outside the invariant Cantor set},
  author = {Victor Kleptsyn and Andrés Navas},
  journal= {arXiv preprint arXiv:2607.11748},
  year   = {2026}
}

Comments

10 pages, 3 figures