Denjoy constructions for fibered homeomorphisms of the torus

DOI10.1090/S0002-9947-09-04914-9zbMath1179.37057arXiv0707.4373OpenAlexW1996298793MaRDI QIDQ3642696

Sylvain Crovisier, Frédéric Le Roux, François Béguin, Tobias Jäger

Publication date: 6 November 2009

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0707.4373

zbMATH Keywords

circle mapminimal setsnon-minimal dynamics

Mathematics Subject Classification ID

Dynamical systems involving maps of the circle (37E10) Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces (37E30)

Related Items (8)

ON ANNULAR MAPS OF THE TORUS AND SUBLINEAR DIFFUSION ⋮ Minimal sets of fibre-preserving maps in graph bundles ⋮ Partially hyperbolic diffeomorphisms on Heisenberg nilmanifolds and holonomy maps ⋮ A construction of almost automorphic minimal sets ⋮ Construction of minimal non-invertible skew-product maps on 2-manifolds ⋮ The rigidity of pseudo-rotations on the two-torus and a question of Norton-Sullivan ⋮ Pointwise partial hyperbolicity in three-dimensional nilmanifolds ⋮ Recurrence of non-resonant homeomorphisms on the torus

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Une méthode pour minorer les exposants de Lyapounov et quelques exemples montrant le caractère local d'un théorème d'Arnold et de Moser sur le tore de dimension 2
• Minimal subsets of projective flows
• A point distal transformation of the torus
• Ergodic reduction of random products of two-by-two matrices
• Dynamics of the quasi-periodic Schrödinger cocycle at the lowest energy in the spectrum
• Reducibility or nonuniform hyperbolicity for quasiperiodic Schrödinger cocycles
• Strange nonchaotic attractors in Harper maps
• Construction of curious minimal uniquely ergodic homeomorphisms on manifolds: the Denjoy–Rees technique
• A Minimal Positive Entropy Homeomorphism of the 2-Torus
• Transitive sets for quasi-periodically forced monotone maps
• Constructions in elliptic dynamics
• The Denjoy type of argument for quasiperiodically forced circle diffeomorphisms
• TOWARDS A CLASSIFICATION FOR QUASIPERIODICALLY FORCED CIRCLE HOMEOMORPHISMS
• Strict Ergodicity and Transformation of the Torus
• Positive Lyapunov exponent and minimality for a class of one-dimensional quasi-periodic Schrödinger equations

This page was built for publication: Denjoy constructions for fibered homeomorphisms of the torus