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Astérisque - Titles - 390 (2017) 101-138

Titles < 2017 < 390

Séminaire Bourbaki, volume 2015/2016, exposés 1104-1119
Astérisque 390 (2017), xi+533 pages
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Presentation, Summary

Exposé 1108 : Entropie sofique
Damien GABORIAU
Astérisque 390 (2017), 101-138
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Résumé :
L'entropie fut introduite en systèmes dynamiques par A. Kolmogorov. Initialement focalisée sur les itérations d'une transformation préservant une mesure finie, la notion fut peu à peu généralisée, jusqu'à embrasser les actions des groupes moyennables ainsi que les actions topologiques. L. Bowen (2008) parvint à franchir la barrière du non moyennable en introduisant l'entropie sofique. Cet invariant rend les mêmes services que l'entropie classique pour les actions mesurées des groupes sofiques (une classe qui contient les groupes résiduellement finis). En 2010, D. Kerr et H. Li mirent au point une version topologique et un principe variationnel.

Mots-clefs : Systèmes dynamiques, théorie ergodique, entropie métrique, entropie topologique, entropie sofique, groupes sofiques.

Abstract:
Exposé 1108 : Sofic entropy
The entropy in dynamical systems was introduced by A. Kolmogorov. Initially dedicated to iterations of one finite measure preserving transformation, the notion was gradually generalized so as to encompass amenable group actions and topological actions. L. Bowen (2008) succeeded in breaking the non-amenable frontier by introducing the sofic entropy. This invariant provides the same services as the classical entropy for the measured actions of the sofic groups (a class which contains the residually finite groups). In 2010, D. Kerr et H. Li established a topological version together with a variational principle.

Keywords: Dynamical systems, ergodic theory, metric entropy, topological entropy, sofic entropy, sofic groups.

Class. math. : 37A35, 28D, 37A15, 37B, 20E15.


ISSN : 0303-1179
Publié avec le concours de : Centre National de la Recherche Scientifique

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