A connectedness result for commuting diffeomorphisms of the interval

Details A connectedness result for commuting diffeomorphisms of the interval A connectedness result for commuting diffeomorphisms of the interval

2009-12-08

arxiv.org/abs/0912.1464v2

Mathematics

Dynamical Systems

10 pages, v2 contains minor exposition improvements and a proof of lemma 4, replacing a reference to another article

Scientific paper

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.

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