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Rigidity of measures—The high entropy case and non-commuting foliations

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Abstract

We consider invariant measures for partially hyperbolic, semisimple, higher rank actions on homogeneous spaces defined by products of real andp-adic Lie groups. In this paper we generalize our earlier work to establish measure rigidity in the high entropy case in that setting. We avoid any additional ergodicity-type assumptions but rely on, and extend the theory of conditional measures.

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Authors and Affiliations

  1. Department of Mathematics, Box 354350, University of Washington, 98195, Seattle, WA, USA

    Manfred Einsiedler

  2. Department of Mathematics, Penn State University, 16802, State College, PA, USA

    Anatole Katok

Authors
  1. Manfred Einsiedler
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  2. Anatole Katok
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Corresponding author

Correspondence to Manfred Einsiedler.

Additional information

To Hillel Furstenberg with friendship and admiration

Manfred Einsiedler is partially supported by the NSF Grant DMS 0400587.

Anatole Katok is partially supported by the NSF Grant DMS 0071339.

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Einsiedler, M., Katok, A. Rigidity of measures—The high entropy case and non-commuting foliations. Isr. J. Math. 148, 169–238 (2005). https://doi.org/10.1007/BF02775436

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  • DOI: https://doi.org/10.1007/BF02775436

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