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15 May 2009 Distribution of periodic torus orbits on homogeneous spaces
Manfred Einsiedler, Elon Lindenstrauss, Philippe Michel, Akshay Venkatesh
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Duke Math. J. 148(1): 119-174 (15 May 2009). DOI: 10.1215/00127094-2009-023

Abstract

We prove results toward the equidistribution of certain families of periodic torus orbits on homogeneous spaces, with particular focus on the case of the diagonal torus acting on quotients of PGLn(R). After attaching to each periodic orbit an integral invariant (the discriminant), our results have the following flavor: certain standard conjectures about the distribution of such orbits hold up to exceptional sets of at most O(Δϵ) orbits of discriminant at most Δ. The proof relies on the well-separatedness of periodic orbits together with measure rigidity for torus actions. We give examples of sequences of periodic orbits of this action that fail to become equidistributed even in higher rank. We also give an application of our results to sharpen a theorem of Minkowski on ideal classes in totally real number fields of cubic and higher degrees

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Manfred Einsiedler. Elon Lindenstrauss. Philippe Michel. Akshay Venkatesh. "Distribution of periodic torus orbits on homogeneous spaces." Duke Math. J. 148 (1) 119 - 174, 15 May 2009. https://doi.org/10.1215/00127094-2009-023

Information

Published: 15 May 2009
First available in Project Euclid: 22 April 2009

zbMATH: 1172.37003
MathSciNet: MR2515103
Digital Object Identifier: 10.1215/00127094-2009-023

Subjects:
Primary: 37A17 , 37A45
Secondary: 11E99

Rights: Copyright © 2009 Duke University Press

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Vol.148 • No. 1 • 15 May 2009
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