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Perturbative techniques of the dynamics in the $C^1$-topology
Post-edited
Authors : Crovisier, Sylvain (Author of the conference)
CIRM (Publisher )
37C05 - Smooth mappings and diffeomorphisms
37C29 - Homoclinic and heteroclinic orbits
37Dxx - Dynamical systems with hyperbolic behavior
CIRM (Publisher )
Abstract :
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.
MSC Codes : 37C05 - Smooth mappings and diffeomorphisms
37C29 - Homoclinic and heteroclinic orbits
37Dxx - Dynamical systems with hyperbolic behavior
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 07/04/16 Conference Date : 21/03/16 Subseries : Research talks arXiv category : Dynamical Systems Mathematical Area(s) : Dynamical Systems & ODE Format : MP4 (.mp4) - HD Video Time : 01:09:39 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2016-03-21_Crovisier.mp4 
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Information on the Event
Event Title : Dynamics of evolution equations / Systèmes dynamiques et problèmes d'évolutionEvent Organizers : Joly, Romain ; Raugel, Geneviève ; Yi, Yingfei Dates : 21/03/16 - 25/03/16 Event Year : 2016 Event URL : http://conferences.cirm-math.fr/1335.html
Citation Data
DOI : 10.24350/CIRM.V.18948803Cite this video as: 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 |
See Also
- [Multi angle] Geometric control and dynamics / Author of the conference Rifford, Ludovic.
- [Multi angle] Dichotomy, the closed range theorem and optimal control / Author of the conference Brunovsky, Pavel.
- [Multi angle] Dissipativity in nonautonomous linear-quadratic control processes / Author of the conference Núñez, Carmen.
- [Multi angle] Dynamics of bounded solutions of parabolic equations on the real line - Part 1 / Author of the conference Polacik, Peter.
Bibliography
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- 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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