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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.

MSC:
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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