Abstract
We prove that if a homeomorphism of a closed orientable surface S has no wandering points and leaves invariant a compact, connected set K which contains no periodic points, then either \({K=S=\mathbb{T}^2}\) , or K is the intersection of a decreasing sequence of annuli. A version for non-orientable surfaces is given.
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Koropecki, A. Aperiodic invariant continua for surface homeomorphisms. Math. Z. 266, 229–236 (2010). https://doi.org/10.1007/s00209-009-0565-0
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DOI: https://doi.org/10.1007/s00209-009-0565-0