English
Distortion elements in groups of interval diffeomorphisms
Multi angle
Auteurs : Eynard-Bontemps, Hélène (Auteur de la Conférence)
CIRM (Editeur )
37C10 - Vector fields, flows, ordinary differential equations
37C15 - Topological and differentiable equivalence, conjugacy, invariants, moduli, classification
37E05 - Maps of the interval (piecewise continuous, continuous, smooth)
57M60 - Group actions in low dimensions
CIRM (Editeur )
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Résumé :
An element g of an abstract group G is a distortion element if there exists a finite family S in G such that g belongs to the subgroup generated by S and the wordlength of gn (w.r.t. S) grows sublinearly in n. In this talk, we will be interested in the distortion elements of the group of Cr orientation-preserving diffeomorphisms of the closed interval, for different values of r. In particular, we will present some natural obstructions to distortion (such that the presence of hyperbolic fixed points in C1 regularity and the positivity of the so-called asymptotic distortion in C2 regularity (and higher)), and we will wonder whether they are the only ones.
Keywords : diffeomorphism; conjugacy; Mather invariant; asymptotic variation; distortion element
Codes MSC : Keywords : diffeomorphism; conjugacy; Mather invariant; asymptotic variation; distortion element
37C10 - Vector fields, flows, ordinary differential equations
37C15 - Topological and differentiable equivalence, conjugacy, invariants, moduli, classification
37E05 - Maps of the interval (piecewise continuous, continuous, smooth)
57M60 - Group actions in low dimensions
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Informations sur la Vidéo
Réalisateur : Recanzone, LucaLangue : Anglais Date de publication : 10/01/2025 Date de captation : 10/12/2024 Sous collection : Research talks arXiv category : Dynamical Systems Domaine : Dynamical Systems & ODE Format : MP4 (.mp4) - HD Durée : 01:00:41 Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2024-12-10_Eynard-Bontemps.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Foliations and Diffeomorphism Groups / Feuilletages et Groupes de DifféomorphismeOrganisateurs de la rencontre : Eynard-Bontemps, Hélène ; Meigniez, Gaël ; Nariman, Sam ; Yazdi, Mehdi Dates : 09/12/2024 - 13/12/2024 Année de la rencontre : 2024 URL Congrès : https://conferences.cirm-math.fr/3082.html
Données de citation
DOI : 10.24350/CIRM.V.20274503Citer cette vidéo: Eynard-Bontemps, Hélène (2024). Distortion elements in groups of interval diffeomorphisms. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20274503 URI : http://dx.doi.org/10.24350/CIRM.V.20274503 |
Voir aussi
- [Multi angle] On the group of real-analytic diffeomorphisms - lecture 3 / Auteur de la Conférence Takashi, Tsuboi.
- [Multi angle] On the group of real-analytic diffeomorphisms - lecture 2 / Auteur de la Conférence Takashi, Tsuboi.
- [Multi angle] On conjugate actions in dimension 1: applications to deformation and distortion - Lecture 3 / Auteur de la Conférence Navas, Andrès.
- [Multi angle] On conjugate actions in dimension 1: applications to deformation and distortion - Lecture 2 / Auteur de la Conférence Navas, Andrès.
- [Multi angle] Groups of Anosov-like homeomorphisms and foliations of the plane - lecture 3 / Auteur de la Conférence Mann, Kathryn.
- [Multi angle] Groups of Anosov-like homeomorphisms and foliations of the plane -Lecture 2 / Auteur de la Conférence Mann, Kathryn.
- [Multi angle] Veering triangulations and transverse foliations / Auteur de la Conférence Zung, Jonathan.
- [Multi angle] On the group of real-analytic diffeomorphisms - Lecture 1 / Auteur de la Conférence Takashi, Tsuboi.
- [Multi angle] Persistently foliar knots / Auteur de la Conférence Roberts, Rachel.
- [Multi angle] On conjugate actions in dimension 1: applications to deformation and distortion - Lecture 1 / Auteur de la Conférence Navas, Andrès.
- [Multi angle] Using ergodic theory to study the cohomology of diffeomorphism groups / Auteur de la Conférence Monod, Nicolas.
- [Multi angle] Dynamics of surface homeomorphisms and fine curve graph / Auteur de la Conférence Militon, Emmanuel.
- [Multi angle] Taut foliations through a contact lens / Auteur de la Conférence Massoni, Thomas.
- [Multi angle] Groups of Anosov-like homeomorphisms and foliations of the plane - lecture 1 / Auteur de la Conférence Mann, Kathryn.
- [Multi angle] Torus homeomorphisms and the fine curve graph / Auteur de la Conférence Le Roux, Frédéric.
- [Multi angle] Critical regularity and subexponential growth / Auteur de la Conférence Kim, Sang-Hyun.
- [Multi angle] Recent progress on groups of area-preserving homeomorphisms / Auteur de la Conférence Humilière, Vincent.
- [Multi angle] Foliations on the plane $ \mathbb{R}^{2}$, pre-laminations on the circle $\mathbb{S}^{1}$, group actions on the circle $\mathbb{S}^{1}$ / Auteur de la Conférence Bonatti, Christian.
Bibliographie
- EYNARD-BONTEMPS, Hélène et NAVAS, Andrés. All, most, some? On diffeomorphisms of the interval that are distorted and/or conjugate to powers of themselves. arXiv preprint arXiv:2405.11366, 2024. - https://doi.org/10.48550/arXiv.2405.11366
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