Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Classification of Minimal Sets of Torus Homeomorphisms   We provide a classification of minimal sets of homeomorphisms of the
two-torus, in terms of the structure of their complement. We show that this
structure is exactly one of the following types: (1) a disjoint union of
topological disks, or (2) a disjoint union of essential annuli and topological
disks, or (3) a disjoint union of one doubly essential component and bounded
topological disks. Periodic bounded disks can only occur in type 3. This result
provides a framework for more detailed investigations, and additional
information on the torus homeomorphism allows to draw further conclusions. In
the non-wandering case, the classification can be significantly strengthened
and we obtain that a minimal set other than the whole torus is either a
periodic orbit, or the orbit of a periodic circloid, or the extension of a
Cantor set. Further special cases are given by torus homeomorphisms homotopic
to an Anosov, in which types 1 and 2 cannot occur, and the same holds for
homeomorphisms homotopic to the identity with a rotation set which has
non-empty interior. If a non-wandering torus homeomorphism has a unique and
totally irrational rotation vector, then any minimal set other than the whole
torus has to be the extension of a Cantor set.

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The categories of this paper are: math-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: nlin
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The categories of this paper are: physics
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: q-fin
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The categories of this paper are: adap-org
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The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: eess
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-lat
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The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas