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

112 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

Access to Document

10.1017/s0143385700009081

Cite this

@article{68fcaa12f3364ac28f80971d8439a52d,

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.",

author = "A. Katok and Spatzier, \{R. J.\}",

year = "1996",

month = aug,

doi = "10.1017/s0143385700009081",

language = "English (US)",

volume = "16",

pages = "751--778",

journal = "Ergodic Theory and Dynamical Systems",

issn = "0143-3857",

publisher = "Cambridge University Press",

number = "4",

}

TY - JOUR

T1 - Invariant measures for higher-rank hyperbolic abelian actions

AU - Katok, A.

AU - Spatzier, R. J.

PY - 1996/8

Y1 - 1996/8

N2 - 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.

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.

UR - https://www.scopus.com/pages/publications/0030520144

UR - https://www.scopus.com/pages/publications/0030520144#tab=citedBy

U2 - 10.1017/s0143385700009081

DO - 10.1017/s0143385700009081

M3 - Article

AN - SCOPUS:0030520144

SN - 0143-3857

VL - 16

SP - 751

EP - 778

JO - Ergodic Theory and Dynamical Systems

JF - Ergodic Theory and Dynamical Systems

IS - 4

ER -

Invariant measures for higher-rank hyperbolic abelian actions

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this