A dichotomy between discrete and continuous spectrum for a class of special flows over rotations | Zendy

Bassam Fayad | Zendy; A. Windsor | Zendy

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A dichotomy between discrete and continuous spectrum for a class of special flows over rotations

Author(s) -

Bassam Fayad,

A. Windsor

Publication year - 2007

Publication title -

journal of modern dynamics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.668

H-Index - 25

eISSN - 1930-532X

pISSN - 1930-5311

DOI - 10.3934/jmd.2007.1.107

Subject(s) - mathematics , irrational number , rigidity (electromagnetism) , topological conjugacy , rotation number , pure mathematics , flow (mathematics) , rotation (mathematics) , mixing (physics) , mathematical analysis , class (philosophy) , geometry , physics , structural engineering , quantum mechanics , artificial intelligence , computer science , engineering

We provide sufficient conditions on a positive function so that the associated special flow over any irrational rotation is either weak mixing or $L^2$-conjugate to a suspension flow. This gives the first such complete classification within the class of Liouville dynamics. This rigidity coexists with a plethora of pathological behaviors.

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