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H 2 Emergence of wandering stable components

Auteurs : Berger, Pierre (Auteur de la Conférence)
CIRM (Editeur )

 Loading the player... Definitions of emergence and entropy Case study of emergence and entropy Program on emergence Taken's last problem Wandering Fatou components Proof of the parameter selection

Résumé : In a joint work with Sebastien Biebler, we show the existence of a locally dense set of real polynomial automorphisms of $\mathbb{C}^{2}$ displaying a stable wandering Fatou component; in particular this solves the problem of their existence, reported by Bedford and Smillie in 1991. These wandering Fatou components have non-empty real trace and their statistical behavior is historical with high emergence. The proof follows from a real geometrical model which enables us to show the existence of an open and dense set of $C^{r}$ families of surface diffeomorphisms in the Newhouse domain, each of which displaying a historical, high emergent, wandering domain at a dense set of parameters, for every $2\leq r\leq \infty$ and $r=\omega$. Hence, this also complements the recent work of Kiriki and Soma, by proving the last Taken's problem in the $C^{\infty }$ and $C^{\omega }$-case.

Keywords : emergence, recurrence stability

Codes MSC :
32Hxx - Holomorphic mappings and correspondences
37Bxx - topological dynamics
37Dxx - Dynamical systems with hyperbolic behavior
37FXX - complex dynamical systems

 Informations sur la Vidéo Réalisateur : Hennenfent, Guillaume Langue : Anglais Date de publication : 23/01/2020 Date de captation : 09/12/2019 Collection : Research talks Format : MP4 (.mp4) - HD Durée : 00:43:08 Domaine : Dynamical Systems & ODE Audience : Chercheurs ; Doctorants , Post - Doctorants Download : https://videos.cirm-math.fr/2019-12-09_berger.mp4 Informations sur la rencontre Nom de la rencontre : Jean-Morlet Chair 2019 - Conference - Thermodynamic Formalism: Dynamical Systems, Statistical Properties and their Applications / Chaire Jean-Morlet 2019 - Conférence - Formalisme thermodynamique : systèmes dynamiques, propriétés statistiques et leurs applicationsOrganisateurs de la rencontre : Nicol, Matthew ; Pollicott, Mark ; Troubetzkoy, Serge ; Vaienti, SandroDates : 09/12/2019 - 13/12/2019 Année de la rencontre : 2019 URL Congrès : https://www.chairejeanmorlet.com/2019-2-... Citation Data DOI : 10.24350/CIRM.V.19586503 Cite this video as: Berger, Pierre (2019). Emergence of wandering stable components. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19586503 URI : http://dx.doi.org/10.24350/CIRM.V.19586503

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