Invariant measures for higher-rank hyperbolic abelian actions

A. Katok; R. J. Spatzier

doi:10.1017/s0143385700009081

Invariant measures for higher-rank hyperbolic abelian actions

A. Katok, R. J. Spatzier

Research output: Contribution to journal › Article › peer-review

111 Scopus citations

Abstract

We investigate invariant ergodic measures for certain partially hyperbolic and Anosov actions of ℝ^k, ℤ^k and ℤ^k₊. We show that they are either Haar measures or that every element of the action has zero metric entropy.

Original language	English (US)
Pages (from-to)	751-778
Number of pages	28
Journal	Ergodic Theory and Dynamical Systems
Volume	16
Issue number	4
DOIs	https://doi.org/10.1017/s0143385700009081
State	Published - Aug 1996

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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title = "Invariant measures for higher-rank hyperbolic abelian actions",

abstract = "We investigate invariant ergodic measures for certain partially hyperbolic and Anosov actions of ℝk, ℤk and ℤk+. We show that they are either Haar measures or that every element of the action has zero metric entropy.",

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year = "1996",

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AU - Spatzier, R. J.

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AB - We investigate invariant ergodic measures for certain partially hyperbolic and Anosov actions of ℝk, ℤk and ℤk+. We show that they are either Haar measures or that every element of the action has zero metric entropy.

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Invariant measures for higher-rank hyperbolic abelian actions

Abstract

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