DYNAMICS OF PSEUDOGROUPS OF ROTATIONS

We study dynamical systems on the circle generated by a finite number of partially defined rotations. We construct new examples with all orb its dense (this leads to non-simplicial free actions of free groups on R-trees). We study the generic dynamics for these pseudogroups and th eir 1-parameter families. We show that, in suitable 2-parameter famili es, the set of pseudogroups having a dense orbit is a Sierpinski curve . We generalize results on interval exchange transformations obtained by Boshernitzan, Veech, Rips.