A connectedness result for commuting diffeomorphisms of the interval
Dynamical Systems
2010-01-04 v2
Abstract
Let D^r_+[0,1], r >= 1, denote the group of orientation-preserving C^r diffeomorphisms of [0,1]. We show that any two representations of Z^2 in D^r_+[0,1], r >= 2, are connected by a continuous path of representations of Z^2 in D^1_+[0,1]. We derive this result from the classical works by G. Szekeres and N. Kopell on the C^1 centralizers of the diffeomorphisms of [0,1) which are at least C^2 and fix only 0.
Keywords
Cite
@article{arxiv.0912.1464,
title = {A connectedness result for commuting diffeomorphisms of the interval},
author = {Helene Eynard},
journal= {arXiv preprint arXiv:0912.1464},
year = {2010}
}
Comments
10 pages, v2 contains minor exposition improvements and a proof of lemma 4, replacing a reference to another article