Toute action d'un groupe de Baumslag-Solitar sur les surfaces a une orbite finie

Guelman, Nancy; Liousse, Isabelle

Document type :

Article dans une revue scientifique: Article original

DOI :

10.1017/etds.2018.23

Permalink :

http://hdl.handle.net/20.500.12210/121765

Title :

Toute action d'un groupe de Baumslag-Solitar sur les surfaces a une orbite finie

Author(s) :

Guelman, Nancy [Auteur]
Liousse, Isabelle [Auteur]

Laboratoire Paul Painlevé - UMR 8524 [LPP]

Journal title :

Ergodic Theory and Dynamical Systems

Pages :

3353-3364

Publisher :

Cambridge University Press (CUP)

Publication date :

2019-12

ISSN :

0143-3857

HAL domain(s) :

Mathématiques [math]

English abstract : [en]

We consider f, h homeomorphims generating a faithful BS(1, n)-action on a closed surface S, that is, hf h-1 = f n , for some n ≥ 2. According to [GL], after replacing f by a suitable iterate if necessary, we can assume ...
Show more >We consider f, h homeomorphims generating a faithful BS(1, n)-action on a closed surface S, that is, hf h-1 = f n , for some n ≥ 2. According to [GL], after replacing f by a suitable iterate if necessary, we can assume that there exists a minimal set Λ of the action, included in F ix(f). Here, we suppose that f and h are C 1 in neighbourhood of Λ and any point x ∈ Λ admits an h-unstable manifold W u (x). Using Bonatti's techniques, we prove that either there exists an integer N such that W u (x) is included in F ix(f N) or there is a lower bound for the norm of the differential of h only depending on n and the Riemannian metric on S. Combining last statement with a result of [AGX], we show that any faithful action of BS(1, n) on S with h a pseudo-Anosov homeomorphism has a finite orbit containing singularities of h ; moreover if f is isotopic to identity it is entirely contained in the singular set of h. As a consequence, there is no faithful C 1-action of BS(1, n) on the torus with h an Anosov.Show less >

Language :

Anglais

Peer reviewed article :

Oui

Audience :

Internationale

Popular science :

Non

ANR Project :

Groupes d'homéomorphismes de variétés
Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

Submission date :

2025-01-24T14:30:20Z

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