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Twist sets for maps of the circle

Published online by Cambridge University Press:  19 September 2008

Michał Misiurewicz
Michał Misiurewicz
Affiliation:
Institute of Mathematics, Warsaw University, 00–901 Warsaw, Poland
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Abstract

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Let f be a continuous map of degree one of the circle onto itself. We prove that for every number a from the rotation interval of f there exists an invariant closed set A consisting of points with rotation number a and such that f restricted to A preserves the order. This result is analogous to the one in the case of a twist map of an annulus.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 4 , Issue 3 , September 1984 , pp. 391 - 404
Copyright
Copyright © Cambridge University Press 1984

References

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