Pages 269-291 from Volume 166 (2007), Issue 1 by Michael Field, Ian Melbourne, Andrei Török
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.
Received: 1 July 2008
Accepted: 31 March 2006
Published online: 1 March 2009
Department of Mathematics, University of Houston, Houston, TX 77004, United States
Department of Mathematics, University of Surrey, Guildford, Surrey, GU2 7XH
Department of Mathematics, University of Houston, Houston, TX 77004, United States and Institute of Mathematics of the Romanian Academy, 014700 Bucharest, Romania