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Stable Ergodicity for Smooth Compact Lie Group Extensions of Hyperbolic Basic Sets

By M Field, I Melbourne and A Torok

Abstract

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

Year: 2005
DOI identifier: 10.1017/S0143385704000355
OAI identifier: oai:epubs.surrey.ac.uk:203

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