Absence of mixing in area-preserving flows on surfaces

Corinna Ulcigrai

Published 2009-01-29Version 1

We prove that minimal area-preserving flows locally given by a smooth Hamiltonian on a closed surface of any genus are typically (in the measure-theoretical sense) not mixing. The result is obtained by considering special flows over interval exchange transformations under roof functions with symmetric logarithmic singularities and proving absence of mixing for a full measure set of interval exchange transformations.