Ergodicity and rigidity for certain subgroups of Diff(omega)(S-1)

We consider the non solvable subgroups of the group of real analytic diffeo morphisms of the circle which admit a finite generating set whose elements belong to an appropriate and fixed neighborhood of the identity. If G is su ch a group, we prove that there are non trivial local analytic vector field s which are a sort of "limit" of some local diffeomorphisms in G. Finally w e apply these vector fields to prove, in particular, that either the group G is ergodic or it has a finite orbit These vector fields also enable us to show that the dynamics of G is topologically rigid. (C) Elsevier, Paris.