Weak mixing for logarithmic flows  over interval exchange transformations

Corinna Ulcigrai

doi:10.3934/jmd.2009.3.35

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2009, Volume 3, Issue 1: 35-49. Doi: 10.3934/jmd.2009.3.35

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Weak mixing for logarithmic flows over interval exchange transformations

Corinna Ulcigrai^1,

1.
School of Mathematics, University of Bristol, Bristol

Received: July 31, 2008

Revised: October 31, 2008

Published: January 2009

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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.

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Mathematics Subject Classification: Primary: 37E35, Secondary: 37A25.

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