Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A zero-one law for dynamical properties   For any countable group $\Gamma$ satisfying the ``weak Rohlin property'', and
for any dynamical property, the set of $\Gamma$-actions with that property is
either residual or meager. The class of groups with the weak Rohlin property
includes each lattice $\integers^{\times{d}}$; indeed, all countable discrete
amenable groups.
  For $\Gamma$ an arbitrary countable group, let $\actsp$ be the set of
$\Gamma$-actions on the unit circle $Y$. We establish an Equivalence theorem by
showing that a dynamical property is Baire/meager/residual in $\actsp$ if and
only if it is Baire/meager/residual in the set of shift-invariant measures on
the product space $Y^{\times\Gamma}$.

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The categories of this paper are: atom-ph
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The categories of this paper are: funct-an
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
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The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
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The categories of this paper are: q-fin
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The categories of this paper are: nlin
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The categories of this paper are: ao-sci
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The categories of this paper are: alg-geom