Minimal sets of non-resonant torus homeomorphisms

Ferry Kwakkel. "Minimal sets of non-resonant torus homeomorphisms." Fundamenta Mathematicae 211.1 (2011): 41-76. <http://eudml.org/doc/283339>.

@article{FerryKwakkel2011,
abstract = {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.},
author = {Ferry Kwakkel},
journal = {Fundamenta Mathematicae},
language = {eng},
number = {1},
pages = {41-76},
title = {Minimal sets of non-resonant torus homeomorphisms},
url = {http://eudml.org/doc/283339},
volume = {211},
year = {2011},
}

TY - JOUR
AU - Ferry Kwakkel
TI - Minimal sets of non-resonant torus homeomorphisms
JO - Fundamenta Mathematicae
PY - 2011
VL - 211
IS - 1
SP - 41
EP - 76
AB - 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.
LA - eng
UR - http://eudml.org/doc/283339
ER -