Dynamics for rotation pseudogroups. (La dynamique des pseudogroupes de rotations.) (French) Zbl 0791.58055

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.


37E10 Dynamical systems involving maps of the circle
37E45 Rotation numbers and vectors
22A22 Topological groupoids (including differentiable and Lie groupoids)
37C85 Dynamics induced by group actions other than \(\mathbb{Z}\) and \(\mathbb{R}\), and \(\mathbb{C}\)
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