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

Adam Kanigowski

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

Dynamical Systems 2013-07-31 v1

Authors: Adam Kanigowski

Abstract

We consider special flows over the rotation on the circle by an irrational $\alpha$ 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 $\alpha$ has bounded partial quotients, we prove that all such flows are weakly mixing and enjoy weak Ratner's property. Moreover, we provide a sufficient condition for the roof function to obtain a stability of the cocycle Ratner's property for the resulting special flow.

Keywords

ratner's property special flows irrational rotations bounded variation weak mixing cantor set

Cite

@article{arxiv.1307.8055,
  title  = {Ratner's property for special flows over irrational rotations under functions of bounded variation. II},
  author = {Adam Kanigowski},
  journal= {arXiv preprint arXiv:1307.8055},
  year   = {2013}
}

Comments

15 pages, this paper is a continuation of arXiv:1302.3429 and arXiv:1002.2734. arXiv admin note: text overlap with arXiv:1002.2734 by other authors

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

Abstract

Keywords

Cite

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