Denjoy constructions for fibred homeomorphisms of the torus - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2007

Denjoy constructions for fibred homeomorphisms of the torus

Résumé

We construct different types of quasiperiodically forced circle homeomorphisms with transitive but non-minimal dynamics. Concerning the recent Poincaré-like classification for this class of maps of Jaeger-Stark, we demonstrate that transitive but non-minimal behaviour can occur in each of the different cases. This closes one of the last gaps in the topological classification. Actually, we are able to get some transitive quasiperiodically forced circle homeomorphisms with rather complicated minimal sets. For example, we show that, in some of the examples we construct, the unique minimal set is a Cantor set and its intersection with each vertical fibre is uncountable and nowhere dense (but may contain isolated points). We also prove that minimal sets of the later kind cannot occur when the dynamics are given by the projective action of a quasiperiodic SL(2,R)-cocycle. More precisely, we show that, for a quasiperiodic SL(2,R)-cocycle, any minimal strict subset of the torus either is a union of finitely many continuous curves, or contains at most two points on generic fibres.
Fichier principal
Vignette du fichier
ffst-25.pdf (367.54 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00165908 , version 1 (30-07-2007)

Identifiants

Citer

François Béguin, Sylvain Crovisier, Tobias Jaeger, Frédéric Le Roux. Denjoy constructions for fibred homeomorphisms of the torus. 2007. ⟨hal-00165908⟩
410 Consultations
51 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More