Ratner’s property for special flows over irrational rotations under functions of bounded variation. II

Adam Kanigowski

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We consider special flows over the rotation on the circle by an irrational α under roof functions of bounded variation. The roof functions, in the Lebesgue decomposition, are assumed to have a continuous singular part coming from a quasi-similar Cantor set (including the devil’s staircase case). Moreover, a finite number of discontinuities is allowed. Assuming that has bounded partial quotients, we prove that all such flows are weakly mixing and enjoy the weak Ratner property. Moreover, we provide a sufficient condition on the roof function for stability of Ratner’s cocycle property of the resulting special flow.

Original languageEnglish (US)
Pages (from-to)125-147
Number of pages23
JournalColloquium Mathematicum
Volume136
Issue number1
DOIs
StatePublished - Jan 1 2014

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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