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

Bassam Fayad; A. Windsor

doi:10.3934/jmd.2007.1.107

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2007, Volume 1, Issue 1: 107-122. Doi: 10.3934/jmd.2007.1.107

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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
2.
University of Texas at Austin, 1 University Station C1200, Austin, TX 78712

Received: April 2006

Published online: October 2006

Abstract / Introduction Related Papers Cited by

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.

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