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January  2007, 1(1): 107-122. doi: 10.3934/jmd.2007.1.107

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

Bassam Fayad 1, and  A. Windsor 2,

1. 

LAGA, CNRS UMR 7539, Université Paris 13, Villetaneuse 93430, France
2. 

University of Texas at Austin, 1 University Station C1200, Austin, TX 78712, United States

Received  April 2006 Published  October 2006

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.
Keywords: time change of linear flows, cohomological theory of dynamical systems, weak mixing..
Mathematics Subject Classification: Primary 37A30; Secondary 37A45, 37E4.
Citation: Bassam Fayad, A. Windsor. A dichotomy between discrete and continuous spectrum for a class of special flows over rotations. Journal of Modern Dynamics, 2007, 1 (1) : 107-122. doi: 10.3934/jmd.2007.1.107
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