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LIAPUNOV STABILITY AND ADDING MACHINES
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UNSPECIFIED (1995) LIAPUNOV STABILITY AND ADDING MACHINES. ERGODIC THEORY AND DYNAMICAL SYSTEMS, 15 (Part 2). pp. 271-290. ISSN 0143-3857.
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Abstract
Let X be a locally connected locally compact metric space and f : X --> X a continuous map. Let A be a compact transitive set under f. If A is asymptotically stable, then it has finitely many connected components, which are cyclically permuted. If it is Liapunov stable, then A may have infinitely many connected components. Our main result states that these form a Canter set on which f is topologically conjugate to an adding machine. A number of consequences are derived, including a complete classification of compact transitive sets for continuous maps of the interval and the Liapunov instability of the invariant Canter set of Denjoy maps of the circle.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Journal or Publication Title: | ERGODIC THEORY AND DYNAMICAL SYSTEMS | ||||
Publisher: | CAMBRIDGE UNIV PRESS | ||||
ISSN: | 0143-3857 | ||||
Official Date: | April 1995 | ||||
Dates: |
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Volume: | 15 | ||||
Number: | Part 2 | ||||
Number of Pages: | 20 | ||||
Page Range: | pp. 271-290 | ||||
Publication Status: | Published |
Data sourced from Thomson Reuters' Web of Knowledge
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