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Connectedness of the space of smooth actions of $\mathbb{Z}^{n}$ on the interval

Published online by Cambridge University Press:  20 April 2015

CHRISTIAN BONATTI  and
HÉLÈNE EYNARD-BONTEMPS
CHRISTIAN BONATTI
Affiliation:
Institut de Mathématiques de Bourgogne, CNRS - UMR 5584, Université de Bourgogne, 9 av. A. Savary, 21000 Dijon, France email bonatti@u-bourgogne.fr
HÉLÈNE EYNARD-BONTEMPS
Affiliation:
IMJ - PRG, CNRS - UMR 7586, Université Pierre et Marie Curie, 4 place Jussieu, 75252 Paris cedex, France email helene.eynard-bontemps@imj-prg.fr
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Abstract

We prove that the spaces of ${\mathcal{C}}^{\infty }$ orientation preserving actions of $\mathbb{Z}^{n}$ on $[0,1]$ and non-free actions of $\mathbb{Z}^{2}$ on the circle are connected.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 36 , Issue 7 , October 2016 , pp. 2076 - 2106
Copyright
© Cambridge University Press, 2015 

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