Journal of Modern Dynamics (JMD)

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

Pages: 107 - 122, Issue 1, January 2007      doi:10.3934/jmd.2007.1.107

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Bassam Fayad - LAGA, CNRS UMR 7539, Université Paris 13, Villetaneuse 93430, France (email)
A. Windsor - University of Texas at Austin, 1 University Station C1200, Austin, TX 78712, United States (email)

Abstract: 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, 37E45.

Received: April 2006;      Available Online: October 2006.