The rotation set of a homeomorphism of the annulus is closed

DOI10.1007/BF02096762zbMath0725.54032OpenAlexW2004357410MaRDI QIDQ2276799

Michael Handel

Publication date: 1990

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02096762

zbMATH Keywords

rotation setclosed annulus

Mathematics Subject Classification ID

Related Items (25)

Topological methods in surface dynamics ⋮ Fully essential dynamics for area-preserving surface homeomorphisms ⋮ Unremovable periodic orbits of homeomorphisms ⋮ About periodic and quasi-periodic orbits of a new type for twist maps of the torus ⋮ Simple braids for surface homeomorphisms ⋮ Lefschetz numbers of periodic orbits of pseudo-Anosov homeomorphisms ⋮ Pseudo solutions, rotation sets, and shadowing rotations for monotone recurrence relations ⋮ ON ANNULAR MAPS OF THE TORUS AND SUBLINEAR DIFFUSION ⋮ Entropy zero area preserving diffeomorphisms of \(S^{2}\) ⋮ Conservative dynamics: unstable sets for saddle-center loops. ⋮ A condition that implies full homotopical complexity of orbits for surface homeomorphisms ⋮ A characterization of annularity for area-preserving toral homeomorphisms ⋮ Chain Transitivity and Rotation Shadowing for Annulus Homeomorphisms ⋮ Realizing rotation numbers on annular continua ⋮ Monotone periodic orbits for torus homeomorphisms ⋮ Area-preserving diffeomorphisms of the torus whose rotation sets have non-empty interior ⋮ Nielsen theory, braids and fixed points of surface homeomorphisms ⋮ Dynamics of field line mappings in magnetic flux tubes ⋮ On period minimal pseudo-Anosov braids ⋮ Rotation numbers and instability sets ⋮ Non-monotone periodic orbits of a rotational horseshoe ⋮ Non‐realizability of the Torelli group as area‐preserving homeomorphisms ⋮ Boundaries of rotation sets for homeomorphisms of the 𝑛-torus ⋮ On non-contractible periodic orbits for surface homeomorphisms ⋮ Non-realizability of the pure braid group as area-preserving homeomorphisms

Cites Work

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• The discrete Frenkel-Kontorova model and its extensions: I. Exact results for the ground-states
• Existence of quasi-periodic orbits for twist homeomorphisms of the annulus
• Global shadowing of pseudo-Anosov homeomorphisms
• On the geometry and dynamics of diffeomorphisms of surfaces
• Rotation shadowing properties of circle and annulus maps

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