Distortion elements in groups of interval diffeomorphisms | Vidéo | Carmin.tv

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Distortion elements in groups of interval diffeomorphisms

By Hélène Eynard-Bontemps

Appears in collection : Foliations and Diffeomorphism Groups / Feuilletages et Groupes de Difféomorphisme

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.

Information about the video

Date of recording 10/12/2024
Date of publication 10/01/2025
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Luca Recanzone
Format MP4

Citation data

DOI 10.24350/CIRM.V.20274503
Cite this video Eynard-Bontemps, Hélène (10/12/2024). Distortion elements in groups of interval diffeomorphisms. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20274503
URL https://dx.doi.org/10.24350/CIRM.V.20274503

Domain(s)

Dynamical Systems

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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