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arXiv · 0912.2896

Perturbation de la dynamique de difféomorphismes en topologie C^1 / Perturbation of the dynamics of diffeomorphisms in the C^1-topology

Sylvain Crovisier
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Abstract

Les travaux présentés dans ce mémoire portent sur la dynamique de difféomorphismes de variétés compactes. Pour l'étude des propriétés génériques ou pour la construction d'exemples, il est souvent utile de savoir perturber un système. Ceci soulève généralement des problèmes délicats : une modification locale de la dynamique peut engendrer un changement brutal du comportement des orbites. En topologie C^1, nous proposons diverses techniques permettant de perturber tout en contrôlant la dynamique : mise en transversalité, connexion d'orbites, perturbation de la dynamique tangente, réalisation d'extensions... Nous en tirons diverses applications à la description de la dynamique des difféomorphismes C^1-génériques. This memoir deals with the dynamics of diffeomorphisms of compact manifolds. For the study of generic properties or for the construction of examples, it is often useful to be able to perturb a system. This generally leads to delicate problems: a local modification of the dynamic may cause a radical change in the behavior of the orbits. For the C^1 topology, we propose various techniques which allow to perturb while controlling the dynamic: setting in transversal position, connection of orbits, perturbation of the tangent dynamics,... We derive various applications to the description of the C^1-generic diffeomorphisms.

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Sylvain Crovisier. 2009-12-15. Perturbation de la dynamique de difféomorphismes en topologie C^1 / Perturbation of the dynamics of diffeomorphisms in the C^1-topology. https://arxiv.org/abs/0912.2896

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