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Emergence of wandering stable components
Post-edited
Authors : Berger, Pierre (Author of the conference)
CIRM (Publisher )
32Hxx - Holomorphic mappings and correspondences
37Bxx - topological dynamics
37Dxx - Dynamical systems with hyperbolic behavior
37FXX - complex dynamical systems
CIRM (Publisher )
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| 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 |
Abstract :
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
MSC Codes : Keywords : emergence; recurrence stability
32Hxx - Holomorphic mappings and correspondences
37Bxx - topological dynamics
37Dxx - Dynamical systems with hyperbolic behavior
37FXX - complex dynamical systems
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 23/01/2020 Conference Date : 09/12/2019 Subseries : Research talks arXiv category : Complex Variables ; Dynamical Systems Mathematical Area(s) : Dynamical Systems & ODE Format : MP4 (.mp4) - HD Video Time : 00:43:08 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2019-12-09_berger.mp4 
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Information on the Event
Event Title : 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 applicationsEvent Organizers : Nicol, Matthew ; Pollicott, Mark ; Troubetzkoy, Serge ; Vaienti, Sandro Dates : 09/12/2019 - 13/12/2019 Event Year : 2019 Event URL : https://www.chairejeanmorlet.com/2109.html
Citation Data
DOI : 10.24350/CIRM.V.19586503Cite 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 |
See Also
- [Multi angle] Besov spaces in multifractal environment, and the Frisch-Parisi conjecture / Author of the conference Seuret, Stéphane.
- [Multi angle] Marked length spectrum rigidity and the geodesic stretch / Author of the conference Knieper, Gerhard.
- [Multi angle] Intermediate dimensions, capacities and projections / Author of the conference Falconer, Kenneth.
- [Multi angle] Closed geodesics and the measure of maximal entropy on surfaces without conjugate points / Author of the conference Climenhaga, Vaughn.
Bibliography
- BERGER, Pierre, BIEBLER, Sébastien. Emergence of wandering stable components. 2020. ⟨hal-02449496⟩ - https://hal.archives-ouvertes.fr/hal-02449496
