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

• Autorzy: Adam Kanigowski
• Języki publikacji: EN

Abstrakty

EN

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 α 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.

Kategorie tematyczne

• 37E35: Flows on surfaces
• 37A25: Ergodicity, mixing, rates of mixing
• 37A10: One-parameter continuous families of measure-preserving transformations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2014
• Tom: 136
• Numer: 1
• Strony: 125-147

Daty

wydano

2014

Twórcy

autor

Adam Kanigowski

• Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-656 Warszawa, Poland

Identyfikatory

DOI

10.4064/cm136-1-11