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Transitivity of Heisenberg group extensions of hyperbolic systems
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Melbourne, Ian, Nijica, Viorel and Torok, Andrei (2012) Transitivity of Heisenberg group extensions of hyperbolic systems. Ergodic Theory and Dynamical Systems, Vol.32 (No.1). pp. 223-235. doi:10.1017/S014338571000091X ISSN 0143-3857.
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Official URL: http://dx.doi.org/10.1017/S014338571000091X
Abstract
We show that among Cr extensions (r>0) of a uniformly hyperbolic dynamical system with fiber the standard real Heisenberg group ℋn of dimension 2n+1, those that avoid an obvious obstruction to topological transitivity are generically topologically transitive. Moreover, if one considers extensions with fiber a connected nilpotent Lie group with a compact commutator subgroup (for example ℋn/ℤ), among those that avoid the obvious obstruction, topological transitivity is open and dense.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
| Journal or Publication Title: | Ergodic Theory and Dynamical Systems | ||||
| Publisher: | Cambridge University Press | ||||
| ISSN: | 0143-3857 | ||||
| Official Date: | 2012 | ||||
| Dates: |
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| Volume: | Vol.32 | ||||
| Number: | No.1 | ||||
| Page Range: | pp. 223-235 | ||||
| DOI: | 10.1017/S014338571000091X | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access |
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