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A connectedness result for commuting diffeomorphisms of the interval

Published online by Cambridge University Press:  04 June 2010

HÉLÈNE EYNARD
HÉLÈNE EYNARD*
Affiliation:
Graduate School of Mathematical Sciences, University of Tokyo, Komaba, Meguro, Tokyo 153-8914, Japan (email: [email protected])
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Abstract

Let 𝒟r+[0,1], r≥1, denote the group of orientation-preserving 𝒞r diffeomorphisms of [0,1]. We show that any two representations of ℤ2 in 𝒟r+[0,1], r≥2, are connected by a continuous path of representations of ℤ2 in 𝒟1+[0,1] . We derive this result from the classical works by G. Szekeres and N. Kopell on the 𝒞1 centralizers of the diffeomorphisms of [0,1) that are at least 𝒞2 and fix only 0 .

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 31 , Issue 4 , August 2011 , pp. 1183 - 1191
Copyright
Copyright © Cambridge University Press 2010

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References

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