English

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}
}