Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On non-contractible periodic orbits for surface homeomorphisms   In this work we study homeomorphisms of closed orientable surfaces homotopic
to the identity, focusing on the existence of non-contractible periodic orbits.
We show that, if $g$ is such a homeomorphism, and if $\hat g$ is its lift to
the universal covering of $S$ that commutes with the deck transformations, then
one of the following three conditions must be satisfied: (1) The set of fixed
points for $\hat g$ projects to a closed subset $F$ which contains an essential
continuum, (2) $g$ has non-contratible periodic points of every sufficiently
large period, or (3) there exists an uniform bound $M$ such that, if $\hat x$
projects to a contractible periodic point then the $\hat g$ orbit of $\hat x$
has diameter less or equal to $M$. Some consequences for homeomorphisms of
surfaces whose rotation set is a singleton are derived.

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The categories of this paper are: physics
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The categories of this paper are: astro-ph
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The categories of this paper are: nlin
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The categories of this paper are: comp-gas
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The categories of this paper are: chem-ph
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The categories of this paper are: math-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: econ
24
The categories of this paper are: dg-ga
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-th
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The categories of this paper are: adap-org
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The categories of this paper are: ao-sci
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The categories of this paper are: atom-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: alg-geom