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Register a new userPerturbation de la dynamique de diffeomorphismes en topologie C^1 / Perturbation of the dynamics of diffeomorphisms in the C^1-topology
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Authors
Sylvain Crovisier
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Les travaux presentes dans ce memoire portent sur la dynamique de diffeomorphismes de varietes compactes. Pour letude des proprietes generiques ou pour la construction dexemples, il est souvent utile de savoir perturber un syst`eme. Ceci soul`eve generalement des probl`emes delicats : 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 contr^olant la dynamique : mise en transversalite, connexion dorbites, perturbation de la dynamique tangente, realisation dextensions... Nous en tirons diverses applications `a la description de la dynamique des diffeomorphismes C^1-generiques. <p> 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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