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Minimal sets of non-resonant torus homeomorphisms
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Kwakkel, Ferry. (2011) Minimal sets of non-resonant torus homeomorphisms. Fundamenta Mathematicae , Vol.211 (No.1). pp. 41-76. ISSN 0016-2736
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Official URL: http://dx.doi.org/10.4064/fm211-1-3
Abstract
As was known to H. Poincare, 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.
| Item Type: | Journal Article |
|---|---|
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Faculty of Science > Mathematics |
| Journal or Publication Title: | Fundamenta Mathematicae |
| Publisher: | Polska Akademia Nauk |
| ISSN: | 0016-2736 |
| Date: | 2011 |
| Volume: | Vol.211 |
| Number: | No.1 |
| Page Range: | pp. 41-76 |
| Identification Number: | 10.4064/fm211-1-3 |
| Status: | Peer Reviewed |
| Publication Status: | Published |
| Access rights to Published version: | Restricted or Subscription Access |
| Funder: | MRTN-CT-2006-035651 |
| URI: | http://wrap.warwick.ac.uk/id/eprint/42097 |
Data sourced from Thomson Reuters' Web of Knowledge
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