BourbakiV1, Main, Exploration, bibRecord, 000007

Sofic entropy, after Lewis Bowen, David Kerr and Hanfeng Li

Identifieur interne : 000007 ( Main/Exploration ); précédent : 000006; suivant : 000008

Sofic entropy, after Lewis Bowen, David Kerr and Hanfeng Li

Auteurs : Damien Gaboriau [France]

Source :

RBID : Hal:hal-01347306

English descriptors

mix :
- dynamical systems, ergodic theory, metric entropy, sofic entropy, sofic groups, topological entropy.

Abstract

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.

Url:

https://hal.archives-ouvertes.fr/hal-01347306

Affiliations:

France

Links toward previous steps (curation, corpus...)

to stream Hal, to step Corpus: 000028
to stream Hal, to step Curation: 000028
to stream Hal, to step Checkpoint: 000004
to stream Main, to step Merge: 000007
to stream Main, to step Curation: 000007

Le document en format XML

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<title xml:lang="fr">Entropie sofique d'après Lewis Bowen, David Kerr et Hanfeng Li</title>
<title xml:lang="fr" type="sub">Séminaire Bourbaki du 16 janvier 2016</title>
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<title xml:lang="fr" type="sub">Séminaire Bourbaki du 16 janvier 2016</title>
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<front><div type="abstract" xml:lang="en">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.</div>
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Sofic entropy, after Lewis Bowen, David Kerr and Hanfeng Li

Sofic entropy, after Lewis Bowen, David Kerr and Hanfeng Li

Source :

English descriptors

Abstract

Links toward previous steps (curation, corpus...)

Le document en format XML

Pour manipuler ce document sous Unix (Dilib)

Pour mettre un lien sur cette page dans le réseau Wicri