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Comptes Rendus Mathématique
Volume 346, n° 3-4
pages 203-208 (février 2008)
Doi : 10.1016/j.crma.2007.11.017
Received : 9 April 2007 ;  accepted : 22 November 2007
Modèles pour les applications fibrées et les polysystèmes
Models for skew-products and polysystems
 

Jean-Pierre Marco
Institut de mathématiques de Jussieu, 175, rue du Chevaleret, 75013 Paris, France 

Résumé

Cette Note donne un analogue du classique « fer à cheval » de Smale, adapté à l’étude des propriétés dynamiques des difféomorphismes possédant des variétés normalement hyperboliques avec intersections homoclines convenables. Notre modèle abstrait donne lieu à l’existence d’applications fibrées au-dessus du décalage de Bernoulli, dont un cas particulier intéressant est celui des polysystèmes, que nous définissons ici, qui peuvent être vus comme itération simultanée de plusieurs applications sur un même espace, dans un ordre quelconque. Pour citer cet article : J.-P. Marco, C. R. Acad. Sci. Paris, Ser. I 346 (2008).

The full text of this article is available in PDF format.
Abstract

We introduce a fibered version of the classical ‘horseshoe’ of Smale, that one can use to analyze the dynamical properties of diffeomorphisms with a normally hyperbolic invariant manifold and suitable homoclinic intersections. Our abstract model gives rise to fibered dynamics over the Bernoulli shift and to the more particular case of polysystems that we define here, which can be seen as the simultaneous iteration of several maps on the same space in any prescribed order. To cite this article: J.-P. Marco, C. R. Acad. Sci. Paris, Ser. I 346 (2008).

The full text of this article is available in PDF format.


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