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 applications

Collection 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 applications

Organizer(s) Nicol, Matthew ; Pollicott, Mark ; Troubetzkoy, Serge ; Vaienti, Sandro

Date(s) 09/12/2019 - 13/12/2019

linked URL https://www.chairejeanmorlet.com/2109.html

00:00:00 / 00:00:00

1 5

Chapters

Emergence of wandering stable components

By Pierre Berger

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.

Information about the video

Date of recording 09/12/2019
Date of publication 23/01/2020
Institution CIRM
Licence CC BY NC ND
Language English
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19586503
Cite this video Berger, Pierre (09/12/2019). Emergence of wandering stable components. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19586503
URL https://dx.doi.org/10.24350/CIRM.V.19586503

Domain(s)

Bibliography

BERGER, Pierre, BIEBLER, Sébastien. Emergence of wandering stable components. 2020. ⟨hal-02449496⟩ - https://hal.archives-ouvertes.fr/hal-02449496

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