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Liapunov stability and adding machines revisited
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Buescu, Jorge, Kulczycki, Marcin and Stewart, Ian (2006) Liapunov stability and adding machines revisited. Dynamical Systems, Vol.21 (No.3). pp. 379-384. doi:10.1080/14689360600649815
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Official URL: http://dx.doi.org/10.1080/14689360600649815
Abstract
We give a revised proof of a theorem originally due to Buescu and Stewart (1995). The new version of this theorem dispenses with the assumption that the space X is locally compact. The theorem is as follows: let X be a locally connected metric space, let f: X -> X be a continuous map, and let A subset of X be a Liapunov stable compact transitive set that has infinitely many connected components. Then the map induced by f on the space of connected components of A is topologically conjugate to an adding machine.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics T Technology > TJ Mechanical engineering and machinery |
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| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
| Journal or Publication Title: | Dynamical Systems | ||||
| Publisher: | Taylor & Francis Ltd. | ||||
| ISSN: | 1468-9367 | ||||
| Official Date: | September 2006 | ||||
| Dates: |
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| Volume: | Vol.21 | ||||
| Number: | No.3 | ||||
| Number of Pages: | 6 | ||||
| Page Range: | pp. 379-384 | ||||
| DOI: | 10.1080/14689360600649815 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access |
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