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Escape of mass and entropy for diagonal flows in real rank one situations

Einsiedler, M. ; Kadyrov, S. ; Pohl, A.

In: Israel Journal of Mathematics, 2015, vol. 210, no. 1, p. 245-295

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    Titre
    • Escape of mass and entropy for diagonal flows in real rank one situations
    Auteur
    • Einsiedler, M.. Departement Mathematik, ETH Zürich, Rämistrasse 101, 8092, Zürich, Switzerland
    • Kadyrov, S.. School of Mathematics, University of Bristol, Bristol, UK
    • Pohl, A.. Mathematisches Institut, Georg-August-Universität Göttingen, Bunsenstr. 3-5, 37073, Göttingen, Germany
    Type de document
    • Postprint
    Langue
    • Anglais
    Publié dans
    • Israel Journal of Mathematics, 2015, vol. 210, no. 1, p. 245-295. The Hebrew University Magnes Press
    Autre version électronique
    Classification
    • Mathématiques
    Identifiant OAI-PMH
    • oai:doc.rero.ch:332571
    Summary
    Let G be a connected semisimple Lie group of real rank 1 with finite center, let Γ be a non-uniform lattice in G and a any diagonalizable element in G. We investigate the relation between the metric entropy of a acting on the homogeneous space Γ\G and escape of mass. Moreover, we provide bounds on the escaping mass and, as an application, we show that the Hausdorff dimension of the set of orbits (under iteration of a) which miss a fixed open set is not full.