  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.
