Absence of mixing in area-preserving flows on surfaces
Dynamical Systems
2009-01-30 v1
Abstract
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.
Keywords
Cite
@article{arxiv.0901.4764,
title = {Absence of mixing in area-preserving flows on surfaces},
author = {Corinna Ulcigrai},
journal= {arXiv preprint arXiv:0901.4764},
year = {2009}
}