Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fully essential dynamics for area-preserving surface homeomorphisms   We study the interplay between the dynamics of area-preserving surface
homeomorphisms homotopic to the identity and the topology of the surface. We
define fully essential dynamics and generalize the results previously obtained
on strictly toral dynamics to surfaces of higher genus. Non-fully essential
dynamics are, in a way, reducible to surfaces of lower genus, while in the
fully essential case the dynamics is decomposed into a disjoint union of
periodic bounded disks and a complementary invariant externally transitive
continuum $C$. When the Misiurewicz-Ziemian rotation set has non-empty interior
the dynamics is fully essential, and the set $C$ is (externally) sensitive on
initial conditions and realizes all the rotational dynamics. As a fundamental
tool we introduce the notion of homotopically bounded sets and we prove a
general boundedness result for invariant open sets when the fixed point set is
inessential.

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The categories of this paper are: astro-ph
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The categories of this paper are: cs
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
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The categories of this paper are: hep-th
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The categories of this paper are: math-ph
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The categories of this paper are: q-fin
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The categories of this paper are: supr-con
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The categories of this paper are: physics
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg