Twist sets for maps of the circle
- 19 September 1984
- journal article
- research article
- Published by Cambridge University Press (CUP) in Ergodic Theory and Dynamical Systems
- Vol. 4 (3) , 391-404
- https://doi.org/10.1017/s0143385700002534
Abstract
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.Keywords
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