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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).


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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.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
Field, M
Torok, A
Date : 1 January 2005
Identification Number : 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=>here</a> to access the journal's website.
Depositing User : Mr Adam Field
Date Deposited : 27 May 2010 14:07
Last Modified : 31 Oct 2017 13:57

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