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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

AZER AKHMEDOV
AZER AKHMEDOV*
Affiliation:
Department of Mathematics, North Dakota State University, Fargo, ND 58108, USA email azer.akhmedov@ndsu.edu
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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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 36 , Issue 5 , August 2016 , pp. 1343 - 1353
Copyright
© Cambridge University Press, 2015 

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