Extension of H\"older's Theorem in Diff_{+}^{1+\epsilon}(I)

Abstract

We prove that if \Gamma is subgroup of Diff_{+}^{1+\epsilon}(I) and N is a natural number such that every non-identity element of \Gamma has at most N fixed points then \Gamma is solvable. If in addition \Gamma is a subgroup of Diff_{+}^{2}(I) then we can claim that \Gamma is metaabelian.