Diffeomorphisms of the Torus with Wandering Domains

DOI10.2307/2159549zbMath0830.54030OpenAlexW4252643977MaRDI QIDQ4039323

Patrick D. McSwiggen

Publication date: 28 January 1996

Full work available at URL: https://doi.org/10.2307/2159549

zbMATH Keywords

wandering domainDenjoy counterexamplestoral diffeomorphism

Mathematics Subject Classification ID

Dynamics induced by group actions other than (mathbb{Z}) and (mathbb{R}), and (mathbb{C}) (37C85) Variational problems concerning extremal problems in several variables; Yang-Mills functionals (58E15) Dynamical systems with hyperbolic behavior (37D99)

Related Items (17)

Conformal irregularity for Denjoy diffeomorphisms of the 2-torus ⋮ Locally connected exceptional minimal sets of surface homeomorphisms. ⋮ The structure of mean equicontinuous group actions ⋮ Rigidity of some abelian-by-cyclic solvable group actions on \({\mathbb{T}}^N\) ⋮ Minimal direct products ⋮ Non-trivial wandering domains for heterodimensional cycles ⋮ On partially hyperbolic diffeomorphisms and regular Denjoy type homeomorphisms ⋮ Wandering domains for diffeomorphisms of the k-torus: a remark on a theorem by Norton and Sullivan ⋮ A few remarks on partially hyperbolic diffeomorphisms of \(\mathbb T^3\) isotopic to Anosov ⋮ Denjoy-Sacksteder theory for groups of diffeomorphisms ⋮ Takens' last problem and existence of non-trivial wandering domains ⋮ The rigidity of pseudo-rotations on the two-torus and a question of Norton-Sullivan ⋮ Local rigidity of Diophantine translations in higher-dimensional tori ⋮ Nonexistence of wandering domains for strongly dissipative infinitely renormalizable Hénon maps at the boundary of chaos ⋮ No round wandering domains for -diffeomorphisms of tori ⋮ On topological classification of regular Denjoy type homeomorphisms ⋮ Historic wandering domains near cycles

Cites Work

• Embedded continued fractals and their Hausdorff dimension
• Denjoy fractals
• Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations. (On smooth conjugacy of diffeomorphisms of the circle with rotations)
• Unsmoothable diffeomorphisms
• Conformal irregularity for Denjoy diffeomorphisms of the 2-torus
• Anosov diffeomorphisms are topologically stable
• Unsmoothable Diffeomorphisms on Higher Dimensional Manifolds
• Diffeomorphisms of thek-torus with wandering domains
• Invariant manifolds

This page was built for publication: Diffeomorphisms of the Torus with Wandering Domains