Aperiodic invariant continua for surface homeomorphisms

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 and S is a torus, or $K$ is the intersection of a decreasing sequence of annuli. A version for non-orientable surfaces is given.

8 pages, to appear in Mathematische Zeitschrift

References in corpus (1)

• Transitivity of generic semigroups of area-preserving surface diffeomorphisms

Cited by in corpus (10)

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• $R$-closed homeomorphisms on surfaces
• Homoclinic orbits for area preserving diffeomorphisms
• A classification of minimal sets for surface homeomorphisms
• A characterization of annularity for area-preserving toral homeomorphisms
• Hénon maps: a list of open problems