Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Dynamical Approach to the Asymptotic Behavior of the Sequence
  $\Omega(n)$   We study the asymptotic behavior of the sequence $\{\Omega(n) \}_{ n \in
\mathbb{N} }$ from a dynamical point of view, where $\Omega(n)$ denotes the
number of prime factors of $n$ counted with multiplicity. First, we show that
for any non-atomic ergodic system $(X, \mathcal{B}, \mu, T)$, the operators
$T^{\Omega(n)}: \mathcal{B} \to L^1(\mu)$ have the strong sweeping-out
property. In particular, this implies that the Pointwise Ergodic Theorem does
not hold along $\Omega(n)$. Second, we show that the behaviors of $\Omega(n)$
captured by the Prime Number Theorem and Erd\H{o}s-Kac Theorem are disjoint, in
the sense that their dynamical correlations tend to zero.

28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
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The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio