Mild mixing property for special flows under piecewise constant functions | Zendy

Krzysztof Fra̧czek | Zendy; Mariusz Lemańczyk | Zendy; Emmanuel Lesigne | Zendy

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Mild mixing property for special flows under piecewise constant functions

Author(s) -

Krzysztof Fra̧czek,

Mariusz Lemańczyk,

Emmanuel Lesigne

Publication year - 2007

Publication title -

discrete and continuous dynamical systems

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.289

H-Index - 70

eISSN - 1553-5231

pISSN - 1078-0947

DOI - 10.3934/dcds.2007.19.691

Subject(s) - mixing (physics) , piecewise , constant (computer programming) , torus , flow (mathematics) , mathematics , property (philosophy) , rotation (mathematics) , mathematical analysis , constant function , irrational number , function (biology) , rotation number , pure mathematics , geometry , physics , computer science , philosophy , epistemology , quantum mechanics , evolutionary biology , biology , programming language

We give a condition on a piecewise constant roof function and an irrational rotation by $\alpha$ on the circle to give rise to a special flow having the mild mixing property. Such flows will also satisfy Ratner's property. As a consequence we obtain a class of mildly mixing singular flows on the two-torus that arise from quasi-periodic Hamiltonians flows by velocity changes.

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