A C∞ Denjoy counterexample

DOI10.1017/S0143385700001243zbMath0501.58035WikidataQ124809939 ScholiaQ124809939MaRDI QIDQ3966819

Glen Richard Hall

Publication date: 1981

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

zbMATH Keywords

Seifert conjecturehomtervalirrational rotation numberinvariant minimal setDenjoy exampleinterval of critical points

Mathematics Subject Classification ID

Differential topological aspects of diffeomorphisms (57R50) Dynamical systems and ergodic theory (37-XX)

Related Items (15)

Transition to topological chaos for circle maps ⋮ Bifurcations of circle maps: Arnol'd tongues, bistability and rotation intervals ⋮ Continued fractals and the Seifert conjecture ⋮ Rigidity of smooth critical circle maps ⋮ Real bounds and Lyapunov exponents ⋮ Integrability of moduli and regularity of Denjoy counterexamples ⋮ Automorphic measures and invariant distributions for circle dynamics ⋮ Dynamics on Ahlfors quasi-circles ⋮ Cherry flows with non-trivial attractors ⋮ Takens' last problem and existence of non-trivial wandering domains ⋮ Nonexistence of wandering domains for strongly dissipative infinitely renormalizable Hénon maps at the boundary of chaos ⋮ A Denjoy counterexample for circle maps with an half-critical point ⋮ Dynamics of multicritical circle maps ⋮ \(C^{\infty}\)-mappings of an interval with attracting cycles of arbitrarily large periods ⋮ There are no σ-finite absolutely continuous invariant measures for multicritical circle maps ^*

Cites Work

• Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations. (On smooth conjugacy of diffeomorphisms of the circle with rotations)

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