Metric properties of measure preserving homeomorphisms

Anatoly Katok, A. M. Stepin

Research output: Contribution to journalArticle

16 Scopus citations

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

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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