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." Colloquium Mathematicae 136.1 (2014): 125-147. <http://eudml.org/doc/284262>.

@article{AdamKanigowski2014,
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 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.},
author = {Adam Kanigowski},
journal = {Colloquium Mathematicae},
keywords = {ratner's property; special flows; weak mixing; devil's staircase. (1) the WR-property has the same dynamical consequences as the original H-property of ratner (see section 3)},
language = {eng},
number = {1},
pages = {125-147},
title = {Ratner's property for special flows over irrational rotations under functions of bounded variation. II},
url = {http://eudml.org/doc/284262},
volume = {136},
year = {2014},
}

TY - JOUR
AU - Adam Kanigowski
TI - Ratner's property for special flows over irrational rotations under functions of bounded variation. II
JO - Colloquium Mathematicae
PY - 2014
VL - 136
IS - 1
SP - 125
EP - 147
AB - 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.
LA - eng
KW - ratner's property; special flows; weak mixing; devil's staircase. (1) the WR-property has the same dynamical consequences as the original H-property of ratner (see section 3)
UR - http://eudml.org/doc/284262
ER -