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Sur les rapprochements par conjugaison en dimension 1 et classe $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}C^1$

Part of: Low-dimensional dynamical systems Representation theory of groups Smooth dynamical systems: general theory

Published online by Cambridge University Press:  19 June 2014

Andrés Navas
Andrés Navas*
Affiliation:
Dpto. de Matemática y C.C., Universidad de Santiago de Chile (USACH), Alameda 3363, Estación Central, 71783-5 Santiago, Chile email andres.navas@usach.cl
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Abstract

We show that the space of actions of every finitely generated, nilpotent group by $C^1$ orientation-preserving diffeomorphisms of the circle is path-connected. This is done via a general result that allows any given action on the interval to be connected to the trivial one by a continuous path of topological conjugates.

Keywords

nilpotent groupconnectednessactions on the interval

MSC classification

Secondary: 20D15: Nilpotent groups, $p$-groups 37C85: Dynamics of group actions other than ${bf Z}$ and ${bf R}$, and foliations 37E99: None of the above, but in this section

Information

Type
Research Article
Information
Compositio Mathematica , Volume 150 , Issue 7 , July 2014 , pp. 1183 - 1195
Copyright
© The Author 2014 

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