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Contracting self-similar groups and conformal dimension
Multi angle
Authors : Nekrashevych, Volodymyr (Author of the conference)
CIRM (Publisher )
CIRM (Publisher )
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Abstract :
One can associate with every finitely generated contracting self-similar group (for example, with the iterated monodromy group of a sub-hyperbolic rational function) and every positive $p$ the associated $\ell_{p}$-contraction coefficient. The critical exponent of the group is the infimum of the set of values of $p$ for which the $\ell_{p}$-contraction coefficient is less than 1. Another number associated with a contracting self-similar group is the Ahlfors-regular conformal dimension of its limit space. One can show that the critical exponent is not greater than the conformal dimension. However, the inequality may be strict. For example, the critical exponent is less than 1 for many groups of intermediate growth (while the corresponding conformal dimension is equal to 1 ). We will also discuss a related notion of the degree of complexity of an action of a group on a set.
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 02/11/2021 Conference Date : 20/09/2021 Subseries : Research talks arXiv category : Group Theory ; Dynamical Systems Mathematical Area(s) : Dynamical Systems & ODE Format : MP4 (.mp4) - HD Video Time : 00:59:08 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2021-09-20_Nekrashevych.mp4 
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Information on the Event
Event Title : Advancing Bridges in Complex Dynamics / Avancer les connections dans la dynamique complexeEvent Organizers : Benini, Anna Miriam ; Drach, Kostiantyn ; Dudko, Dzmitry ; Hlushchanka, Mikhail ; Schleicher, Dierk Dates : 20/09/2021 - 24/09/2021 Event Year : 2021 Event URL : https://conferences.cirm-math.fr/2546.html
Citation Data
DOI : 10.24350/CIRM.V.19813903Cite this video as: Nekrashevych, Volodymyr (2021). Contracting self-similar groups and conformal dimension . CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19813903 URI : http://dx.doi.org/10.24350/CIRM.V.19813903 |
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