Minimal sets of non-resonant torus homeomorphisms

• Autorzy: Ferry Kwakkel
• Języki publikacji: EN

Abstrakty

EN

As was known to H. Poincaré, an orientation preserving circle homeomorphism without periodic points is either minimal or has no dense orbits, and every orbit accumulates on the unique minimal set. In the first case the minimal set is the circle, in the latter case a Cantor set. In this paper we study a two-dimensional analogue of this classical result: we classify the minimal sets of non-resonant torus homeomorphisms, that is, torus homeomorphisms isotopic to the identity for which the rotation set is a point with rationally independent irrational coordinates.

Kategorie tematyczne

• 37B99: None of the above, but in this section
• 37B45: Continua theory in dynamics

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2011
• Tom: 211
• Numer: 1
• Strony: 41-76

Daty

wydano

2011

Twórcy

autor

Ferry Kwakkel

• Mathematics Institute, University of Warwick, CV4 7AL, Coventry, United Kingdom

Identyfikatory

DOI

10.4064/fm211-1-3