- Titel
- On torus homeomorphisms semiconjugate to irrational rotations
- Zitierfähige Url:
- https://nbn-resolving.org/urn:nbn:de:bsz:14-qucosa2-390515
- Quellenangabe
- Ergodic theory and dynamical systems Erscheinungsort: Cambridge
Verlag: Cambridge University Press
Erscheinungsjahr: 2015
Jahrgang: 35
Heft: 7
Seiten: 2114-2137
ISSN: 0143-3857
E-ISSN: 1469-4417 - Erstveröffentlichung
- 2015
- Abstract (EN)
- In the context of the Franks–Misiurewicz conjecture, we study homeomorphisms of the two-torus semiconjugate to an irrational rotation of the circle. As a special case, this conjecture asserts uniqueness of the rotation vector in this class of systems. We first characterize these maps by the existence of an invariant ‘foliation’ by essential annular continua (essential subcontinua of the torus whose complement is an open annulus) which are permuted with irrational combinatorics. This result places the considered class close to skew products over irrational rotations. Generalizing a well-known result of Herman on forced circle homeomorphisms, we provide a criterion, in terms of topological properties of the annular continua, for the uniqueness of the rotation vector. As a byproduct, we obtain a simple proof for the uniqueness of the rotation vector on decomposable invariant annular continua with empty interior. In addition, we collect a number of observations on the topology and rotation intervals of invariant annular continua with empty interior.
- Andere Ausgabe
- Link zum Artikel der zuerst in der Zeitschrift 'Ergodic theory and dynamical systems' erschienen ist
DOI: 10.1017/etds.2014.23 - Freie Schlagwörter (DE)
- Franks-Misiurewicz-Vermutung, Homöomorphismen, invarianten 'Foliierung', Rotationsvektor
- Freie Schlagwörter (EN)
- Franks-Misiurewicz conjecture, homeomorphisms, invariant 'foliation', rotation vector
- Klassifikation (DDC)
- 510
- Verlag
- Cambridge University Press, Cambridge
- Förder- / Projektangaben
- German Research Council Emmy-Noether grant
ID: JA 1721/2-1 - Version / Begutachtungsstatus
- publizierte Version / Verlagsversion
- URN Qucosa
- urn:nbn:de:bsz:14-qucosa2-390515
- Veröffentlichungsdatum Qucosa
- 17.04.2020
- Dokumenttyp
- Artikel
- Sprache des Dokumentes
- Englisch
- Lizenz / Rechtehinweis
