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.
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