RIGIDITY OF REAL-ANALYTIC ACTIONS OF SL(n, Z) ON Tn: A CASE OF REALIZATION OF ZIMMER PROGRAM

Anatole Katok; Federico Rodriguez Hertz

doi:10.3934/dcds.2010.27.609

RIGIDITY OF REAL-ANALYTIC ACTIONS OF SL(n, Z) ON Tn: A CASE OF REALIZATION OF ZIMMER PROGRAM

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Abstract

We prove that any real-analytic action of SL(n, Z), n ≥ 3 with standard homotopy data that preserves an ergodic measure µ whose support is not contained in a ball, is analytically conjugate on an open invariant set to the standard linear action on the complement to a finite union of periodic orbits.

Original language	English (US)
Title of host publication	The Collected Works of Anatole Katok
Subtitle of host publication	In 2 Volumes
Publisher	World Scientific Publishing Co.
Pages	1975-1981
Number of pages	7
Volume	2
ISBN (Electronic)	9789811238079
ISBN (Print)	9789811238062
DOIs	https://doi.org/10.3934/dcds.2010.27.609
State	Published - Jan 1 2024

All Science Journal Classification (ASJC) codes

General Mathematics
General Engineering

Access to Document

10.3934/dcds.2010.27.609

Cite this

@inbook{5c3829975cba43c391863111be6d89cd,

title = "RIGIDITY OF REAL-ANALYTIC ACTIONS OF SL(n, Z) ON Tn: A CASE OF REALIZATION OF ZIMMER PROGRAM",

abstract = "We prove that any real-analytic action of SL(n, Z), n ≥ 3 with standard homotopy data that preserves an ergodic measure µ whose support is not contained in a ball, is analytically conjugate on an open invariant set to the standard linear action on the complement to a finite union of periodic orbits.",

author = "Anatole Katok and Hertz, \{Federico Rodriguez\}",

note = "Publisher Copyright: {\textcopyright} 2010 American Institute of Mathematical Sciences.",

year = "2024",

month = jan,

day = "1",

doi = "10.3934/dcds.2010.27.609",

language = "English (US)",

isbn = "9789811238062",

volume = "2",

pages = "1975--1981",

booktitle = "The Collected Works of Anatole Katok",

publisher = "World Scientific Publishing Co.",

address = "United States",

}

TY - CHAP

T1 - RIGIDITY OF REAL-ANALYTIC ACTIONS OF SL(n, Z) ON Tn

T2 - A CASE OF REALIZATION OF ZIMMER PROGRAM

AU - Katok, Anatole

AU - Hertz, Federico Rodriguez

PY - 2024/1/1

Y1 - 2024/1/1

N2 - We prove that any real-analytic action of SL(n, Z), n ≥ 3 with standard homotopy data that preserves an ergodic measure µ whose support is not contained in a ball, is analytically conjugate on an open invariant set to the standard linear action on the complement to a finite union of periodic orbits.

AB - We prove that any real-analytic action of SL(n, Z), n ≥ 3 with standard homotopy data that preserves an ergodic measure µ whose support is not contained in a ball, is analytically conjugate on an open invariant set to the standard linear action on the complement to a finite union of periodic orbits.

UR - https://www.scopus.com/pages/publications/85195948919

UR - https://www.scopus.com/inward/citedby.url?scp=85195948919&partnerID=8YFLogxK

U2 - 10.3934/dcds.2010.27.609

DO - 10.3934/dcds.2010.27.609

M3 - Chapter

AN - SCOPUS:85195948919

SN - 9789811238062

VL - 2

SP - 1975

EP - 1981

BT - The Collected Works of Anatole Katok

PB - World Scientific Publishing Co.

ER -

RIGIDITY OF REAL-ANALYTIC ACTIONS OF SL(n, Z) ON Tn: A CASE OF REALIZATION OF ZIMMER PROGRAM

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this