Transitivity and the centre for maps of the circle
- 1 March 1986
- journal article
- research article
- Published by Cambridge University Press (CUP) in Ergodic Theory and Dynamical Systems
- Vol. 6 (1) , 1-8
- https://doi.org/10.1017/s0143385700003254
Abstract
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.Keywords
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