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

Manfred Einsiedler; Anatole Katok

doi:10.1007/BF02775436

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

Manfred Einsiedler, Anatole Katok

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Abstract

We consider invariant measures for partially hyperbolic, semisimple, higher rank actions on homogeneous spaces defined by products of real and p-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.

Original language	English (US)
Pages (from-to)	169-238
Number of pages	70
Journal	Israel Journal of Mathematics
Volume	148
DOIs	https://doi.org/10.1007/BF02775436
State	Published - 2005

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1007/BF02775436

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title = "Rigidity of measures - The high entropy case and non-commuting foliations",

abstract = "We consider invariant measures for partially hyperbolic, semisimple, higher rank actions on homogeneous spaces defined by products of real and p-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.",

author = "Manfred Einsiedler and Anatole Katok",

note = "Funding Information: * Manfred Einsiedler is partially supported by the NSF Grant DMS 0400587. ** Anatole Katok is partially supported by the NSF Grant DMS 0071339. Received March 7, 2004 and in revised form October 14, 2004",

year = "2005",

doi = "10.1007/BF02775436",

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volume = "148",

pages = "169--238",

journal = "Israel Journal of Mathematics",

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AU - Einsiedler, Manfred

AU - Katok, Anatole

N1 - Funding Information: * Manfred Einsiedler is partially supported by the NSF Grant DMS 0400587. ** Anatole Katok is partially supported by the NSF Grant DMS 0071339. Received March 7, 2004 and in revised form October 14, 2004

PY - 2005

Y1 - 2005

N2 - We consider invariant measures for partially hyperbolic, semisimple, higher rank actions on homogeneous spaces defined by products of real and p-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.

AB - We consider invariant measures for partially hyperbolic, semisimple, higher rank actions on homogeneous spaces defined by products of real and p-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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U2 - 10.1007/BF02775436

DO - 10.1007/BF02775436

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AN - SCOPUS:32544452370

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VL - 148

SP - 169

EP - 238

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

ER -

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

Abstract

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