Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Construction of curious minimal uniquely ergodic homeomorphisms on
  manifolds: the Denjoy-Rees technique   Mary Rees has constructed a minimal homeomorphism of the 2-torus with
positive topological entropy. This homeomorphism f is obtained by enriching the
dynamics of an irrational rotation R. We improve Rees construction, allowing to
start with any homeomorphism R instead of an irrational rotation and to control
precisely the measurable dynamics of f. This yields in particular the following
result: Any compact manifold of dimension d>1 which carries a minimal uniquely
ergodic homeomorphism also carries a minimal uniquely ergodic homeomorphism
with positive topological entropy. More generally, given some homeomorphism R
of a (compact) manifold and some homeomorphism h of a Cantor set, we construct
a homeomorphism f which "looks like" R from the topological viewpoint and
"looks like" R*h from the measurable viewpoint. This construction can be seen
as a partial answer to the following realisability question: which measurable
dynamical systems are represented by homeomorphisms on manifolds ?

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The categories of this paper are: nlin
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-bio
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The categories of this paper are: atom-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: eess
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The categories of this paper are: q-alg
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-lat
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The categories of this paper are: gr-qc
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The categories of this paper are: math-ph
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The categories of this paper are: ao-sci
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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: quant-ph