Stable Ergodicity for Smooth Compact Lie Group Extensions of Hyperbolic Basic Sets
Field, M, Melbourne, I and Torok, A (2005) Stable Ergodicity for Smooth Compact Lie Group Extensions of Hyperbolic Basic Sets Ergodic Theory and Dynamical Systems, 25 (2).
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 > 0 (here r need not be an integer and C-1 is replaced by Lipschitz). Moreover, when r >= 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.
|Divisions :||Faculty of Engineering and Physical Sciences > Mathematics|
|Date :||1 January 2005|
|Identification Number :||https://doi.org/10.1017/S0143385704000355|
|Additional Information :||Published in <i>Ergodic Theory and Dynamical Systems,</i> Vol 25, Pt. 2. Copyright 2005 Cambridge University Press. Click <a href=http://journals.cambridge.org>here</a> to access the journal's website.|
|Depositing User :||Mr Adam Field|
|Date Deposited :||27 May 2010 14:07|
|Last Modified :||23 Sep 2013 18:26|
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