Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Higher Order Oscillating Sequences, Affine Distal Flows on the
  $d$-Torus, and Sarnak's Conjecture   In this paper, we give two precise definitions of a higher order oscillating
sequence and show the importance of this concept in the study of Sarnak's
conjecture. We prove that any higher order oscillating sequence of order $d$ is
linearly disjoint from all affine distal flows on the $d$-torus for all $d\geq
2$. One consequence of this result is that any higher order oscillating
sequence of order $2$ is linearly disjoint from all affine flows on the
$2$-torus with zero topological entropy. In particular, this reconfirms
Sarnak's conjecture for all affine flows on the $2$-torus with zero topological
entropy and for all affine distal flows on the $d$-torus for all $d\geq 2$.

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The categories of this paper are: cs
29
The categories of this paper are: funct-an
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The categories of this paper are: physics
31
The categories of this paper are: ao-sci
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The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: q-bio
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The categories of this paper are: hep-lat
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The categories of this paper are: cond-mat
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The categories of this paper are: adap-org
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The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn