Rigidity of measures -- the high entropy case and non-commuting foliations
type: Item
instance of: scholarly article
title: Rigidity of measures -- the high entropy case and non-commuting foliations
zbMATH Open document ID: 1097.37017
DOI: 10.1007/BF02775436
author: Manfred Einsiedler
author: Anatole Katok
published in: Israel Journal of Mathematics
publication date: 2006-02-06T00:00:00Z
review text: This paper continues the program (started in [the second author and \textit{R. J. Spatzier}, Ergodic Theory Dyn. Syst. 16, 751--778 (1996); correction ibid. 18, 503--507 (1998; Zbl 0859.58021)]) of studying invariant measures for hyperbolic actions of higher rank abelian groups based on the considerations of entropy and conditional measures on invariant foliations. In particular, results on measure rigidity obtained earlier are generalized in the high entropy case. The theory of conditional measures is extended as well.
reviewed by: Michael L. Blank
Mathematics Subject Classification ID: 37D25
Mathematics Subject Classification ID: 28D20
Mathematics Subject Classification ID: 37C85
Mathematics Subject Classification ID: 37A35
zbMATH DE Number: 5003409
zbMATH Keywords: invariant measures
zbMATH Keywords: hyperbolic actions
zbMATH Keywords: rigidity
zbMATH Keywords: entropy
zbMATH Keywords: invariant foliations
MaRDI profile type: Publication
cites work: Multi-Invariant Sets on Tori
cites work: Multi-Invariant Sets on Compact Abelian Groups
cites work: Q4012688
cites work: Q3843151
cites work: Uniform distribution of horocycle orbits for Fuchsian groups
cites work: Invariant measures on G/Γ for split simple Lie groups G
cites work: Invariant measures and the set of exceptions to Littlewood's conjecture
cites work: Rigidity properties of ℤ^{𝕕}-actions on tori and solenoids
cites work: Joinings of higher-rank diagonalizable actions on locally homogeneous spaces
cites work: A generalization of a result of R. Lyons about measures on \([0,1)\)
cites work: Disjointness in ergodic theory, minimal sets, and a problem in diophantine approximation
cites work: Q5671414
cites work: Normal numbers, entropy, translations
cites work: Q4044675
cites work: Measures on the circle invariant under multiplication by a nonlacunary subsemigroup of the integers
cites work: Invariant measures for actions of higher rank abelian groups
cites work: Rigidity of the measurable structure for algebraic actions of higher-rank Abelian groups
cites work: Invariant measures for higher-rank hyperbolic abelian actions
cites work: The metric entropy of diffeomorphisms. II: Relations between entropy, exponents and dimension
cites work: Q3635940
cites work: On sets invariant under the action of the diagonal group
cites work: On measures simultaneously 2- and 3-invariant
cites work: Q3829606
cites work: Invariant measures for actions of unipotent groups over local fields on homogeneous spaces
cites work: Q4880546
cites work: On Raghunathan's measure conjecture
cites work: Raghunathan's topological conjecture and distributions of unipotent flows
cites work: Raghunathan's conjectures for \(SL(2,{\mathbb{R}{}})\)
cites work: Q4865968
cites work: Raghunathan's conjectures for Cartesian products of real and \(p\)-adic Lie groups
cites work: ×2 and ×3 invariant measures and entropy
full work available at URL: https://doi.org/10.1007/bf02775436
OpenAlex ID: W2098449382
description: scientific article; zbMATH DE number 5003409