Weak mixing for logarithmic flows over interval exchange transformations
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.
Received: August 2008; Revised: November 2008; Published: February 2009.