Absence of mixing in area-preserving flows on surfaces

Corinna Ulcigrai

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arXiv · 0901.4764

Absence of mixing in area-preserving flows on surfaces

Corinna Ulcigrai

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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.

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Corinna Ulcigrai. 2009-01-29. Absence of mixing in area-preserving flows on surfaces. https://arxiv.org/abs/0901.4764

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