Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nearly Continuous Even Kakutani Equivalence of Strongly Rank One
  Transformations   In ergodic theory, two systems are Kakutani equivalent if there exists a
conjugacy between induced transformations. In Measured Topological Orbit and
Kakutani Equivalence, del Junco, Rudolph, and Weiss defined nearly continuous
even Kakutani equivalence as an orbit equivalence which restricts to a
conjugacy between induced maps on nearly clopen sets. This paper defines nearly
continuous even Kakutani equivalence between two nearly continuous dynamical
systems as a nearly continuous conjugacy between induced maps on nearly clopen
sets of the same size and shows that this definition is equivalent to the
definition given by del Junco, Rudolph, and Weiss. The paper shows that, with
an added restriction, if two systems are nearly continuously (non-even)
Kakutani equivalent, then one system is isomorphic to an induced transformation
of the other, and uses this result to prove that a class of transformations
called strongly rank one and containing Chacon's map belongs to the same nearly
continuous even Kakutani equivalence class as irrational rotations.

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The categories of this paper are: atom-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
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The categories of this paper are: hep-lat
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The categories of this paper are: adap-org
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The categories of this paper are: nlin
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The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
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The categories of this paper are: math-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: astro-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: quant-ph