Journal of Modern Dynamics (JMD)

Weak mixing for logarithmic flows over interval exchange transformations

Pages: 35 - 49, Issue 1, January 2009      doi:10.3934/jmd.2009.3.35

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Corinna Ulcigrai - School of Mathematics, University of Bristol, Bristol, United Kingdom (email)

Abstract: We consider a class of special flows over interval exchange transformations which includes roof functions with symmetric logarithmic singularities. We prove that such flows are typically weakly mixing. As a corollary, minimal flows given by multivalued Hamiltonians on higher-genus surfaces are typically weakly mixing.

Keywords:  Weak mixing, interval exchange transformations, logarithmic singularities, area-preserving flows on surfaces.
Mathematics Subject Classification:  Primary: 37E35, Secondary: 37A25.

Received: August 2008;      Revised: November 2008;      Available Online: February 2009.