Weak mixing for logarithmic flows over interval exchange transformations

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January 2009, 3(1): 35-49. doi: 10.3934/jmd.2009.3.35

Weak mixing for logarithmic flows over interval exchange transformations

1.	School of Mathematics, University of Bristol, Bristol, United Kingdom

Received August 2008 Revised November 2008 Published February 2009

Abstract
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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: logarithmic singularities, area-preserving flows on surfaces., Weak mixing, interval exchange transformations.

Mathematics Subject Classification: Primary: 37E35, Secondary: 37A2.

Citation: Corinna Ulcigrai. Weak mixing for logarithmic flows over interval exchange transformations. Journal of Modern Dynamics, 2009, 3 (1) : 35-49. doi: 10.3934/jmd.2009.3.35

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