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Extension of Hölder’s theorem in 
$\text{Diff}_{+}^{\,1+{\it\epsilon}}(I)$
Published online by Cambridge University Press: 11 February 2015
Abstract
We prove that if 
${\rm\Gamma}$ is a subgroup of 
$\text{Diff}_{+}^{\,1+{\it\epsilon}}(I)$ and 
$N$ is a natural number such that every non-identity element of 
${\rm\Gamma}$ has at most 
$N$ fixed points, then 
${\rm\Gamma}$ is solvable. If in addition 
${\rm\Gamma}$ is a subgroup of 
$\text{Diff}_{+}^{\,2}(I)$, then we can claim that 
${\rm\Gamma}$ is meta-abelian.
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- Research Article
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- © Cambridge University Press, 2015
References
Akhmedov, A.. A weak Zassenhaus lemma for subgroups of Diff(I). Algebr. Geom. Topol.
14(1) (2014), 539–550.Google Scholar
Barbot, T.. Characterization des flots d’Anosov en dimension 3 par leurs feuilletages faibles. Ergod. Th. & Dynam. Sys.
15(2) (1995), 247–270.Google Scholar
Farb, B. and Franks, J.. Groups of homeomorphisms of one-manifolds II: extension of Hölder’s theorem. Trans. Amer. Math. Soc.
355(11) (2003), 4385–4396.Google Scholar
Kovacevic, N.. Möbius-like groups of homeomorphisms of the circle. Trans. Amer. Math. Soc.
351(12) (1999), 4791–4822.Google Scholar
Navas, A.. Groups of Circle Diffeomorphisms
(Chicago Lectures in Mathematics)
. University of Chicago Press, Chicago, 2011.Google Scholar