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Arnoux, Pierre

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

Bull. Soc. Math. Fr. 116, No. 4, 489-500 (1988).
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

Cited in 2 Reviews
Cited in 26 Documents

MSC:

37D99 Dynamical systems with hyperbolic behavior

Keywords:

n-torus; semi-conjugacy; interval exchange; pseudo-Anosov diffeomorphism; hyperbolic diffeomorphism
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\textit{P. Arnoux}, Bull. Soc. Math. Fr. 116, No. 4, 489--500 (1988; Zbl 0703.58045)
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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
[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
[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
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