Effectivity of uniqueness of the maximal entropy measure on p-adic homogeneous spaces
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2016-09
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Journal Article
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Abstract
We consider the dynamical system given by an Ad-diagonalizable element a of
the Qp-points G of a unimodular linear algebraic group acting by translation on a finite
volume quotient X. Assuming that this action is exponentially mixing (e.g. if G is simple)
we give an effective version (in terms of K-finite vectors of the regular representation)
of the following statement: If µ is an a-invariant probability measure with measure theoretical entropy close to the topological entropy of a, then µ is close to the unique
G-invariant probability measure of X.
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published
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36 (6)
Pages / Article No.
1972 - 1988
Publisher
Cambridge University Press
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03826 - Einsiedler, Manfred L. / Einsiedler, Manfred L.
Notes
It was possible to publish this article open access thanks to a Swiss National Licence with the publisher.