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La dynamique des pseudogroupes de rotations

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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 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.

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Authors and Affiliations

  1. Mathématique, URA CNRS 1408, Université Paul Sabatier, 118, route de Narbonne, F-31062, Toulouse Cedex, France

    Gilbert Levitt

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  1. Gilbert Levitt
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Oblatum I-1991 & 10-III-1993

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Levitt, G. La dynamique des pseudogroupes de rotations. Invent Math 113, 633–670 (1993). https://doi.org/10.1007/BF01244321

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