ESCAPE OF MASS AND ENTROPY FOR DIAGONAL FLOWS IN REAL RANK ONE SITUATIONS
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Date
2014
Authors
Journal Title
Journal ISSN
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Publisher
ISRAEL JOURNAL OF MATHEMATICS
Abstract
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.
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Keywords
Variation of height, Coordinate system for G, Common cusp excursions of nearby points
Citation
Einsiedler M , Kadyrov S , Pohl A / ESCAPE OF MASS AND ENTROPY FOR DIAGONAL FLOWS IN REAL RANK ONE SITUATIONS / ISRAEL JOURNAL OF MATHEMATICS / 2014