Absence of mixing in area-preserving flows on surfaces

Details Absence of mixing in area-preserving flows on surfaces Absence of mixing in area-preserving flows on surfaces

2009-01-29

arxiv.org/abs/0901.4764v1

Mathematics

Dynamical Systems

Scientific paper

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.

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