Interval exchange transformations and some special flows are not mixing

Anatoly Katok

Research output: Contribution to journalArticlepeer-review

87 Scopus citations

Abstract

An interval exchange transformation (I.E.T.) is a map of an interval into itself which is one-to-one and continuous except for a finite set of points and preserves Lebesgue measure. We prove that any I.E.T. is not mixing with respect to any Borel invariant measure. The same is true for any special flow constructed by any I.E.T. and any "roof" function of bounded variation. As an application of the last result we deduce that in any polygon with the angles commensurable with π the billiard flow is not mixing on two-dimensional invariant manifolds.

Original languageEnglish (US)
Pages (from-to)301-310
Number of pages10
JournalIsrael Journal of Mathematics
Volume35
Issue number4
DOIs
StatePublished - Dec 1 1980

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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