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La distance de réarrangement, duale de la fonctionnelle de Bowen

Published online by Cambridge University Press:  05 April 2011

THIERRY BOUSCH
THIERRY BOUSCH*
Affiliation:
Laboratoire de Mathématique (UMR 8628 CNRS), bât. 425/430, Université Paris-Sud, 91405 Orsay Cedex, France (email: [email protected])
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Abstract

On the space of signed invariant measures of Aℕ, one constructs a norm (and hence a distance) that seems to have a particular significance in dynamics. I shall present some of its properties, in particular a duality theorem à la Kantorovich–Rubinshtein, which gives an expression of this distance using couplings.

Résumé

Sur l’espace des mesures invariantes signées de Aℕ, on construit une norme (et donc une distance) qui semble avoir une importance particulière du point de vue dynamique. Je présenterai quelques-unes de ses propriétés, et tout particulièrement un théorème de dualité à la Kantorovitch–Rubinshtein, qui permet d’exprimer cette distance en termes de couplages.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 32 , Issue 3 , June 2012 , pp. 845 - 868
Copyright
Copyright © Cambridge University Press 2011

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