On disjointness properties of some smooth flows

Krzysztof Frączek, and Mariusz Lemańczyk. "On disjointness properties of some smooth flows." Fundamenta Mathematicae 185.2 (2005): 117-142. <http://eudml.org/doc/282764>.

@article{KrzysztofFrączek2005,
abstract = { Special flows over some locally rigid automorphisms and under L² ceiling functions satisfying a local L² Denjoy-Koksma type inequality are considered. Such flows are proved to be disjoint (in the sense of Furstenberg) from mixing flows and (under some stronger assumption) from weakly mixing flows for which the weak closure of the set of all instances consists of indecomposable Markov operators. As applications we prove that ∙ special flows built over ergodic interval exchange transformations and under functions of bounded variation are disjoint from mixing flows; ∙ ergodic components of flows coming from billiards on rational polygons are disjoint from mixing flows; ∙ smooth ergodic flows of compact orientable smooth surfaces having only non-degenerate saddles as isolated critical points (and having a "good" transversal) are disjoint from mixing and from Gaussian flows. },
author = {Krzysztof Frączek, Mariusz Lemańczyk},
journal = {Fundamenta Mathematicae},
keywords = {special flows; Gaussian flows on smooth compact surfaces; distinguishing dynamics; indecomposable Markov operators},
language = {eng},
number = {2},
pages = {117-142},
title = {On disjointness properties of some smooth flows},
url = {http://eudml.org/doc/282764},
volume = {185},
year = {2005},
}

TY - JOUR
AU - Krzysztof Frączek
AU - Mariusz Lemańczyk
TI - On disjointness properties of some smooth flows
JO - Fundamenta Mathematicae
PY - 2005
VL - 185
IS - 2
SP - 117
EP - 142
AB - Special flows over some locally rigid automorphisms and under L² ceiling functions satisfying a local L² Denjoy-Koksma type inequality are considered. Such flows are proved to be disjoint (in the sense of Furstenberg) from mixing flows and (under some stronger assumption) from weakly mixing flows for which the weak closure of the set of all instances consists of indecomposable Markov operators. As applications we prove that ∙ special flows built over ergodic interval exchange transformations and under functions of bounded variation are disjoint from mixing flows; ∙ ergodic components of flows coming from billiards on rational polygons are disjoint from mixing flows; ∙ smooth ergodic flows of compact orientable smooth surfaces having only non-degenerate saddles as isolated critical points (and having a "good" transversal) are disjoint from mixing and from Gaussian flows.
LA - eng
KW - special flows; Gaussian flows on smooth compact surfaces; distinguishing dynamics; indecomposable Markov operators
UR - http://eudml.org/doc/282764
ER -