Free subgroups of diffeomorphism groups

Abstract

It is proved that the group Diff^k(X) of all C^k-diffeomorphisms of a given C^k-manifold X(k=1,2,...,inf) includes a non-trivial arcwise connected with respect to the Whitney C^k-topology free subgroup which consists (except for the identity) of diffeomorphisms which embed in no flow. It is also proved that for each sequence of elements of Diff^k(X) there are diffeomorphisms arbitrarily close to the given ones which freely generate a subgroup in Diff^k(X).