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Un exemple de semi-conjugaison entre un échange d’intervalles et une translation sur le tore. (An example of semi-conjugacy between an interval exchange and a translation on the torus.). (French) Zbl 0703.58045
A construction is presented of a continuous and surjective semi-conjugacy between an interval exchange and a translation on the 2-dimensional torus which extends to a semi-conjugacy between a pseudo-Anosov diffeomorphism on a genus 3 surface and a hyperbolic diffeomorphism of the 3-dimensional torus.
Reviewer: D.Repovš

MSC:
37D99 Dynamical systems with hyperbolic behavior
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References:
[1] ARNOUX (P.) . - Thèse de 3e cycle , Université de Reims, 1981 .
[2] ARNOUX (P.) et YOCCOZ (J.C.) . - Construction de difféomorphismes pseudo-Anosov , C. R. Acad. Sci. Paris, t. 292, 1981 , p. 75-78. MR 82b:57018 | Zbl 0478.58023 · Zbl 0478.58023
[3] FATHI (A.) . - Some compact invariant sets for hyperbolic linear automorphisms of torii , Ergodic Theory Dynamical Systems, t. 8, 1988 , p. 191-204. MR 90j:58116 | Zbl 0658.58028 · Zbl 0658.58028 · doi:10.1017/S0143385700004417
[4] FATHI (A.) , LAUDENBACH (F.) et POENARU (V.) . - Travaux de Thurston sur les surfaces . - Astérisque 66-67, 1979 .
[5] RAUZY (G.) . - Nombres algébriques et substitutions , Bull. Soc. Math. France, t. 110, 1982 , p. 147-178. Numdam | MR 84h:10074 | Zbl 0522.10032 · Zbl 0522.10032 · numdam:BSMF_1982__110__147_0 · eudml:87410
[6] VEECH (W.A.) . - Gauss measures for transformations on the space of interval exchange maps , Ann. of Math., t. 115, 1982 , p. 201-242. MR 83g:28036b | Zbl 0486.28014 · Zbl 0486.28014 · doi:10.2307/1971391
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