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A remark on the topological entropy and invariant circles of an area preserving twistmap. (English) Zbl 0769.58036
Twist mappings and their applications, Proc. Workshop, Minneapolis/MN (USA) 1989/90, IMA Vol. Math. Appl. 44, 1-5 (1992).
[For the entire collection see Zbl 0745.00054.]
Area preserving twist homeomorphisms $$f: A\longrightarrow A$$ of the annulus $$A = S^ 1 \times {[0,1]}$$ are considered such that the boundary components $$A_ j = S^ 1\times\{j\}$$ are invariant under $$f$$. For such an $$f$$ let $$\rho_ j$$ be the rotation number of the restriction of $$f$$ on $$A_ j$$. It is proved that if $$h_{top} (f) = 0$$, then for every $$\omega\in (\rho_ 0,\rho_ 1)$$, $$f$$ has an invariant circle of rotation number $$\omega$$. Two proofs of this fact are presented the first of which is a simple consequence of results of D. Hall and P. Boyland.
Reviewer: L.Stoyanov (Perth)

##### MSC:
 37A99 Ergodic theory 54C70 Entropy in general topology
##### Keywords:
twist map; topological entropy; invariant circle