Metric properties of measure preserving homeomorphisms

Anatoly Katok, A. M. Stepin

Research output: Contribution to journalArticle

16 Citations (Scopus)

Abstract

We study "typical” metric (ergodic) properties of measure preserving homéo- morphisms of regularly connected cellular polyhedra and of some other spaces. In 1941 Oxtoby and Ulam proved (for a narrower class of spaces) that ergodicity is such a property. Using a modification of their construction and the method of approximating metric automorphisms by periodic ones, we prove in this paper that almost all properties that are "typical” for the metric automorphisms of the Lebesgue spaces are also “typical " for the situation under discussion.

Original languageEnglish (US)
Pages (from-to)191-220
Number of pages30
JournalRussian Mathematical Surveys
Volume25
Issue number2
DOIs
StatePublished - Apr 30 1970

Fingerprint

Metric
Automorphisms
Lebesgue Space
Ergodicity
Morphisms
Polyhedron
Class

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Katok, Anatoly ; Stepin, A. M. / Metric properties of measure preserving homeomorphisms. In: Russian Mathematical Surveys. 1970 ; Vol. 25, No. 2. pp. 191-220.
@article{a7a561790a1348debf068839969908e3,
title = "Metric properties of measure preserving homeomorphisms",
abstract = "We study {"}typical” metric (ergodic) properties of measure preserving hom{\'e}o- morphisms of regularly connected cellular polyhedra and of some other spaces. In 1941 Oxtoby and Ulam proved (for a narrower class of spaces) that ergodicity is such a property. Using a modification of their construction and the method of approximating metric automorphisms by periodic ones, we prove in this paper that almost all properties that are {"}typical” for the metric automorphisms of the Lebesgue spaces are also “typical {"} for the situation under discussion.",
author = "Anatoly Katok and Stepin, {A. M.}",
year = "1970",
month = "4",
day = "30",
doi = "10.1070/RM1970v025n02ABEH003793",
language = "English (US)",
volume = "25",
pages = "191--220",
journal = "Russian Mathematical Surveys",
issn = "0036-0279",
publisher = "IOP Publishing Ltd.",
number = "2",

}

Metric properties of measure preserving homeomorphisms. / Katok, Anatoly; Stepin, A. M.

In: Russian Mathematical Surveys, Vol. 25, No. 2, 30.04.1970, p. 191-220.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Metric properties of measure preserving homeomorphisms

AU - Katok, Anatoly

AU - Stepin, A. M.

PY - 1970/4/30

Y1 - 1970/4/30

N2 - We study "typical” metric (ergodic) properties of measure preserving homéo- morphisms of regularly connected cellular polyhedra and of some other spaces. In 1941 Oxtoby and Ulam proved (for a narrower class of spaces) that ergodicity is such a property. Using a modification of their construction and the method of approximating metric automorphisms by periodic ones, we prove in this paper that almost all properties that are "typical” for the metric automorphisms of the Lebesgue spaces are also “typical " for the situation under discussion.

AB - We study "typical” metric (ergodic) properties of measure preserving homéo- morphisms of regularly connected cellular polyhedra and of some other spaces. In 1941 Oxtoby and Ulam proved (for a narrower class of spaces) that ergodicity is such a property. Using a modification of their construction and the method of approximating metric automorphisms by periodic ones, we prove in this paper that almost all properties that are "typical” for the metric automorphisms of the Lebesgue spaces are also “typical " for the situation under discussion.

UR - http://www.scopus.com/inward/record.url?scp=3042523964&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=3042523964&partnerID=8YFLogxK

U2 - 10.1070/RM1970v025n02ABEH003793

DO - 10.1070/RM1970v025n02ABEH003793

M3 - Article

AN - SCOPUS:3042523964

VL - 25

SP - 191

EP - 220

JO - Russian Mathematical Surveys

JF - Russian Mathematical Surveys

SN - 0036-0279

IS - 2

ER -