On disjointness properties of some smooth flows

• Autorzy: Krzysztof Frączek , Mariusz Lemańczyk
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 37E35: Flows on surfaces
• 37C40: Smooth ergodic theory, invariant measures
• 37A10: One-parameter continuous families of measure-preserving transformations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2005
• Tom: 185
• Numer: 2
• Strony: 117-142

Daty

wydano

2005

Twórcy

autor

Krzysztof Frączek

• Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Chopina 12/18, 87-100 Toruń, Poland

autor

Mariusz Lemańczyk

• Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Chopina 12/18, 87-100 Toruń, Poland

Identyfikatory

DOI

10.4064/fm185-2-2