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Ensembles invariants non enlacés des difféomorphismes du tore et de l’anneau

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Abstract

We introduce the notion of unlinked invariant set for a diffeomorphism of the 2-torus or the closed annulus and we look at the properties of these sets which generalize the Aubry-Mather sets. We prove that for any irrational number ρ in the rotation set of an area-preserving diffeomorphism of the annulus, there exists an unliked invariant set whose rotation set is reduced to ρ. In the same way we prove that any minimal diffeomorphism of the 2-torus homotopic to the identity may be approximated in the C 0-topology by a periodic diffeomorphism.

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Authors and Affiliations

  1. Laboratoire Analyse, Géométrie et Applications, C.N.R.S.-U.M.R 7539, Institut Galilée, Université Paris 13, Avenue J.-B. Clément, 93430, Villetaneuse, France

    Patrice Le Calvez

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  1. Patrice Le Calvez
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Correspondence to Patrice Le Calvez.

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Mathematics Subject Classification (2000)

37E30, 37E45, 37J10

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Le Calvez, P. Ensembles invariants non enlacés des difféomorphismes du tore et de l’anneau. Invent. math. 155, 561–603 (2004). https://doi.org/10.1007/s00222-003-0330-7

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  • DOI: https://doi.org/10.1007/s00222-003-0330-7

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