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Authors : Nekrashevych, Volodymyr (Author of the conference)
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

ℓ_{p}

-contraction coefficient. The critical exponent of the group is the infimum of the set of values of

p

for which the

ℓ_{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, Guillaume

Language :

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Download :

https://videos.cirm-math.fr/2021-09-20_Nekrashevych.mp4

Information on the Event

Event Title : Advancing Bridges in Complex Dynamics / Avancer les connections dans la dynamique complexe
Event 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.19813903
Cite 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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Bibliography

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