Geodesic
Absence of mixing in area-preserving flows on surfaces
Corinna Ulcigrai1
1 Department of Mathematics<br/>University of Bristol<br/> Bristol BS8 1TW<br/> United Kingdom
Annals of mathematics, Tome 173 (2011) no. 3, pp. 1743-1778.

Voir la notice de l'article provenant de la source Annals of Mathematics website

We prove that minimal area-preserving flows locally given by a smooth Hamiltonian on a closed surface of genus $g\geq2$ 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. As a corollary, minimal flows given by multi-valued Hamiltonians on higher genus surfaces which are minimal and have only simple non-degenerate saddles are typically not mixing.
DOI : 10.4007/annals.2011.173.3.10

Corinna Ulcigrai 1

1 Department of Mathematics<br/>University of Bristol<br/> Bristol BS8 1TW<br/> United Kingdom 
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Corinna Ulcigrai. Absence of mixing in area-preserving flows on surfaces. Annals of mathematics, Tome 173 (2011) no. 3, pp. 1743-1778. doi : 10.4007/annals.2011.173.3.10. http://geodesic.mathdoc.fr/articles/10.4007/annals.2011.173.3.10/

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