Geodesic
Stability of mixing and rapid mixing for hyperbolic flows
Michael Field1 ; Ian Melbourne2 ; Andrei Török3
1 Department of Mathematics, University of Houston, Houston, TX 77004, United States
2 Department of Mathematics, University of Surrey, Guildford, Surrey, GU2 7XH<br/>United Kingdom
3 Department of Mathematics, University of Houston, Houston, TX 77004, United States and Institute of Mathematics of the Romanian Academy, 014700 Bucharest, Romania
Annals of mathematics, Tome 166 (2007) no. 1, pp. 269-291.

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

We obtain general results on the stability of mixing and rapid mixing (superpolynomial decay of correlations) for hyperbolic flows. Amongst $C^r$ Axiom A flows, $r\ge2$, we show that there is a $C^2$-open, $C^r$-dense set of flows for which each nontrivial hyperbolic basic set is rapid mixing. This is the first general result on the stability of rapid mixing (or even mixing) for Axiom A flows that holds in a $C^r$, as opposed to Hölder, topology.
DOI : 10.4007/annals.2007.166.269

Michael Field 1 ; Ian Melbourne 2 ; Andrei Török 3

1 Department of Mathematics, University of Houston, Houston, TX 77004, United States
2 Department of Mathematics, University of Surrey, Guildford, Surrey, GU2 7XH<br/>United Kingdom
3 Department of Mathematics, University of Houston, Houston, TX 77004, United States and Institute of Mathematics of the Romanian Academy, 014700 Bucharest, Romania 
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Michael Field; Ian Melbourne; Andrei Török. Stability of mixing and rapid mixing for hyperbolic flows. Annals of mathematics, Tome 166 (2007) no. 1, pp. 269-291. doi : 10.4007/annals.2007.166.269. http://geodesic.mathdoc.fr/articles/10.4007/annals.2007.166.269/

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