Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A family of distal functions and multipliers for strict ergodicity   We give two proofs to an old result of E. Salehi, showing that the Weyl
subalgebra $\mathcal{W}$ of $\ell^\infty(\mathbb{Z})$ is a proper subalgebra of
$\mathcal{D}$, the algebra of distal functions. We also show that the family
$\mathcal{S}^d$ of strictly ergodic functions in $\mathcal{D}$ does not form an
algebra and hence in particular does not coincide with $\mathcal{W}$. We then
use similar constructions to show that a function which is a multiplier for
strict ergodicity, either within $\mathcal{D}$ or in general, is necessarily a
constant. An example of a metric, strictly ergodic, distal flow is constructed
which admits a non-strictly ergodic $2$-fold minimal self-joining. It then
follows that the enveloping group of this flow is not strictly ergodic (as a
$T$-flow). Finally we show that the distal, strictly ergodic Heisenberg
nil-flow is relatively disjoint over its largest equicontinuous factor from
$|\mathcal{W}|$.

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The categories of this paper are: physics
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The categories of this paper are: bayes-an
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The categories of this paper are: acc-phys
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The categories of this paper are: q-alg
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The categories of this paper are: cond-mat
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The categories of this paper are: quant-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: eess
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The categories of this paper are: stat
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-ex