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Transitivity of Euclidean-type extensions of hyperbolic systems
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Melbourne, Ian, Nitica, V. and Torok, Andrei (2009) Transitivity of Euclidean-type extensions of hyperbolic systems. Ergodic Theory and Dynamical Systems, Vol.29 (No.5). pp. 1585-1602. doi:10.1017/S0143385708000886
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Official URL: http://dx.doi.org/10.1017/S0143385708000886
Abstract
Let f:X→X be the restriction to a hyperbolic basic set of a smooth diffeomorphism. We show that in the class of Cr(r>0) cocycles with fiber the special Euclidean group SE(n), those that are transitive form a residual set (countable intersection of open dense sets). This result is new for odd values of n≥3. More generally, we consider Euclidean-type groups Gn where G is a compact connected Lie group acting linearly on n. When Fix G={0}, it is again the case that the transitive cocycles are residual. When Fix G≠{0}, the same result holds upon restriction to the subset of cocycles that avoid an obvious and explicit obstruction to transitivity.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Divisions: | Faculty of Science > Mathematics | ||||
| Journal or Publication Title: | Ergodic Theory and Dynamical Systems | ||||
| Publisher: | Cambridge University Press | ||||
| ISSN: | 0143-3857 | ||||
| Official Date: | 2009 | ||||
| Dates: |
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| Volume: | Vol.29 | ||||
| Number: | No.5 | ||||
| Page Range: | pp. 1585-1602 | ||||
| DOI: | 10.1017/S0143385708000886 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access |
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