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Transitivity and the centre for maps of the circle

Published online by Cambridge University Press:  19 September 2008

Ethan M. Coven  and
Irene Mulvey
Ethan M. Coven
Affiliation:
Department of Mathematics, Wesleyan University, Middletown, CT 06457, USA
Irene Mulvey
Affiliation:
Department of Mathematics, Swarthmore College, Swarthmore, PA 19081, USA
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Abstract

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We study the dynamics of continuous maps of the circle with periodic points. We show that the centre is the closure of the periodic points and that the depth of the centre is at most two. We also characterize the property that every power is transitive in terms of transitivity of a single power and some periodic data.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 6 , Issue 1 , March 1986 , pp. 1 - 8
Copyright
Copyright © Cambridge University Press 1986

References

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