English
Perturbative techniques of the dynamics in the $C^1$-topology
Post-edited
Auteurs : Crovisier, Sylvain (Auteur de la Conférence)
CIRM (Editeur )
37C05 - Smooth mappings and diffeomorphisms
37C29 - Homoclinic and heteroclinic orbits
37Dxx - Dynamical systems with hyperbolic behavior
CIRM (Editeur )
Résumé :
These lectures will address the dynamics of vector fields or 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 dynamics may cause a radical change in the behavior of the orbits. For the $C^1$-topology, various techniques have been developed which allow to perturb while controlling the dynamics: closing and connection of orbits, perturbation of the tangent dynamics... We derive various applications to the description of $C^1$-generic diffeomorphisms.
Codes MSC : 37C05 - Smooth mappings and diffeomorphisms
37C29 - Homoclinic and heteroclinic orbits
37Dxx - Dynamical systems with hyperbolic behavior
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 07/04/16 Date de captation : 21/03/16 Sous collection : Research talks arXiv category : Dynamical Systems Domaine : Dynamical Systems & ODE Format : MP4 (.mp4) - HD Durée : 01:09:39 Audience : Researchers Download : https://videos.cirm-math.fr/2016-03-21_Crovisier.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Dynamics of evolution equations / Systèmes dynamiques et problèmes d'évolutionOrganisateurs de la rencontre : Joly, Romain ; Raugel, Geneviève ; Yi, Yingfei Dates : 21/03/16 - 25/03/16 Année de la rencontre : 2016 URL Congrès : http://conferences.cirm-math.fr/1335.html
Données de citation
DOI : 10.24350/CIRM.V.18948803Citer cette vidéo: Crovisier, Sylvain (2016). Perturbative techniques of the dynamics in the $C^1$-topology. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18948803 URI : http://dx.doi.org/10.24350/CIRM.V.18948803 |
Voir aussi
- [Multi angle] Geometric control and dynamics / Auteur de la Conférence Rifford, Ludovic.
- [Multi angle] Dichotomy, the closed range theorem and optimal control / Auteur de la Conférence Brunovsky, Pavel.
- [Multi angle] Dissipativity in nonautonomous linear-quadratic control processes / Auteur de la Conférence Núñez, Carmen.
- [Multi angle] Dynamics of bounded solutions of parabolic equations on the real line - Part 1 / Auteur de la Conférence Polacik, Peter.
Bibliographie
- Arnaud, M.-C. (1998). Le “closing lemma” en topologie $C^1$. Mémoires de la Société Mathématique de France. Nouvelle Série, 74, 1-120 - https://eudml.org/doc/94925
- Bonatti, C. (2011). Towards a global view of dynamical systems, for the $C^1$-topology. Ergodic Theory and Dynamical Systems, 31(4), 959-993 - http://dx.doi.org/10.1017/S0143385710000891
- Bonatti, C., Díaz, L.J., & Viana, M. (2004). Dynamics beyond uniform hyperbolicity: A global geometric and probabilistic perspective. Berlin: Springer - http://dx.doi.org/10.1007/b138174
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- Crovisier, S. (2013). Perturbation de la dynamique de difféomorphismes en topologie $C^1$. Paris: Société Mathématique de France. (Astérisque, 354) - http://smf4.emath.fr/Publications/Asterisque/2013/354/html/smf_ast_354.php
- Crovisier, S. (2014). Dynamics of $C^1$-diffeomorphisms: global description and prospects for classification. In S.Y. Jang, Y.R. Kim, D.-W. Lee, & I. Yie (Eds.), Proceedings of the International Congress of Mathematicians (ICM 2014). Volume III: Invited lectures (pp. 571-595). Seoul: KM Kyung Moon SA - http://www.icm2014.org/download/download.asp?fn=Proceedings_Volume_III.pdf
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