Dynamics for rotation pseudogroups (Q1319239)

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