English

Classification of generic semigroup actions of circle diffeomorphisms

Dynamical Systems 2018-04-04 v1

Abstract

We study topological properties of semi-group actions on the circle by orientation-preserving homeomorhisms. We prove that a generic action either possesses a forward-invariant interval-domain (i.e. a finite union of disjoint circle arcs), or is two-sided minimal (and, moreover, by a small perturbation one can create a map with arbitrary rotation number in the semigroup). For the minimal case, we also study conditions required for global synchronization.

Keywords

Cite

@article{arxiv.1804.00951,
  title  = {Classification of generic semigroup actions of circle diffeomorphisms},
  author = {Victor Kleptsyn and Yury Kudryashov and Alexey Okunev},
  journal= {arXiv preprint arXiv:1804.00951},
  year   = {2018}
}

Comments

23 pages

R2 v1 2026-06-23T01:12:38.443Z