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Distortion elements in groups of interval diffeomorphisms
Multi angle
Authors : Eynard-Bontemps, Hélène (Author of the conference)
CIRM (Publisher )
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 (Publisher )
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Abstract :
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
MSC Codes : 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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Information on the Video
Film maker : Recanzone, LucaLanguage : English Available date : 10/01/2025 Conference Date : 10/12/2024 Subseries : Research talks arXiv category : Dynamical Systems Mathematical Area(s) : Dynamical Systems & ODE Format : MP4 (.mp4) - HD Video Time : 01:00:41 Targeted 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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Information on the Event
Event Title : Foliations and Diffeomorphism Groups / Feuilletages et Groupes de DifféomorphismeEvent Organizers : Eynard-Bontemps, Hélène ; Meigniez, Gaël ; Nariman, Sam ; Yazdi, Mehdi Dates : 09/12/2024 - 13/12/2024 Event Year : 2024 Event URL : https://conferences.cirm-math.fr/3082.html
Citation Data
DOI : 10.24350/CIRM.V.20274503Cite this video as: 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 |
See Also
- [Multi angle] On the group of real-analytic diffeomorphisms - lecture 3 / Author of the conference Takashi, Tsuboi.
- [Multi angle] On the group of real-analytic diffeomorphisms - lecture 2 / Author of the conference Takashi, Tsuboi.
- [Multi angle] On conjugate actions in dimension 1: applications to deformation and distortion - Lecture 3 / Author of the conference Navas, Andrès.
- [Multi angle] On conjugate actions in dimension 1: applications to deformation and distortion - Lecture 2 / Author of the conference Navas, Andrès.
- [Multi angle] Groups of Anosov-like homeomorphisms and foliations of the plane - lecture 3 / Author of the conference Mann, Kathryn.
- [Multi angle] Groups of Anosov-like homeomorphisms and foliations of the plane -Lecture 2 / Author of the conference Mann, Kathryn.
- [Multi angle] Veering triangulations and transverse foliations / Author of the conference Zung, Jonathan.
- [Multi angle] On the group of real-analytic diffeomorphisms - Lecture 1 / Author of the conference Takashi, Tsuboi.
- [Multi angle] Persistently foliar knots / Author of the conference Roberts, Rachel.
- [Multi angle] On conjugate actions in dimension 1: applications to deformation and distortion - Lecture 1 / Author of the conference Navas, Andrès.
- [Multi angle] Using ergodic theory to study the cohomology of diffeomorphism groups / Author of the conference Monod, Nicolas.
- [Multi angle] Dynamics of surface homeomorphisms and fine curve graph / Author of the conference Militon, Emmanuel.
- [Multi angle] Taut foliations through a contact lens / Author of the conference Massoni, Thomas.
- [Multi angle] Groups of Anosov-like homeomorphisms and foliations of the plane - lecture 1 / Author of the conference Mann, Kathryn.
- [Multi angle] Torus homeomorphisms and the fine curve graph / Author of the conference Le Roux, Frédéric.
- [Multi angle] Critical regularity and subexponential growth / Author of the conference Kim, Sang-Hyun.
- [Multi angle] Recent progress on groups of area-preserving homeomorphisms / Author of the conference Humilière, Vincent.
- [Multi angle] Foliations on the plane $ \mathbb{R}^{2}$, pre-laminations on the circle $\mathbb{S}^{1}$, group actions on the circle $\mathbb{S}^{1}$ / Author of the conference Bonatti, Christian.
Bibliography
- 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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