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Stable ergodicity for smooth compact Lie group extensions of hyperbolic basic sets

Field, Michael, Melbourne, Ian and Török, Andrei (2005) Stable ergodicity for smooth compact Lie group extensions of hyperbolic basic sets Dynamical Systems, 25. pp. 517-551.

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Abstract

<p>We obtain sharp results for the genericity and stability of transitivity, ergodicity and mixing for compact connected Lie group extensions over a hyperbolic basic set of a <i>C</i><sup>2</sup> diffeomorphism. In contrast to previous work, our results hold for general hyperbolic basic sets and are valid in the <i>C<sup>r</sup></i>-topology for all <i>r</i> > 0 (here <i>r</i> need not be an integer and <i>C</i><sup>1</sup> is replaced by Lipschitz). Moreover, when <i>r</i> is greater than or equal to 2, we show that there is a <i>C</i><sup>2</sup>-open and <i>C<sup>r</sup></i>-dense subset of <i>C<sup>r</sup></i>-extensions that are ergodic. We obtain similar results on stable transitivity for (non-compact) <b>R</b><sup><i>m</sup></i>-extensions, thereby generalizing a result of Nitica and Pollicott, and on stable mixing for suspension flows.</p>

Item Type: Article
Additional Information: Published in Ergodic Theory and Dynamical Systems, Vol. 25, pp. 517-551. © 2005 Cambridge University Press. Reprinted with permission.
Divisions: Faculty of Engineering and Physical Sciences > Mathematics
Depositing User: Mr Adam Field
Date Deposited: 27 May 2010 14:41
Last Modified: 23 Sep 2013 18:33
URI: http://epubs.surrey.ac.uk/id/eprint/1485

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