Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Switched server systems whose parameters are normal numbers in base 4   Switched server systems are mathematical models of manufacturing, traffic and
queueing systems. Recently, it was proved in (Eur. J. Appl. Math. 31(4) (2020),
pp. 682-708) that there exist switched server systems with $3$ buffers (tanks),
a server, filling rates $\rho_1=\rho_2=\rho_3=\frac13$ and parameters $d_1,
d_2, d_3>0$ whose global attractor is a fractal set. In this article, we prove
that if $x_1$ in $(0,\frac13)$, $x_2$ in $(\frac13,\frac23)$ and $x_3$ in
$(\frac23,1)$ are rational numbers or normal numbers in base $4$ (or more
generally, rich numbers to base $4$) and $(d_1,d_2,d_3)$ is the vector with
positive entries satisfying $$d_1=\frac{1}{3x_1}-1,\quad
d_2=\frac{2-3x_2}{3x_2-1}, \quad d_3=\frac{3-3x_3}{3x_3-2},$$ then the
corresponding switched server has no fractal attractor. More precisely, the
Poincar\'e map of the system has a finite global attractor. The approach we use
is to study the topological dynamics of a family of piecewise $\lambda$-affine
contractions that includes the Poincar\'e map of the switched server system as
a particular case.

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The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
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The categories of this paper are: q-alg
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The categories of this paper are: patt-sol
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The categories of this paper are: chao-dyn
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The categories of this paper are: nlin
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The categories of this paper are: astro-ph
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The categories of this paper are: econ
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The categories of this paper are: mtrl-th
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The categories of this paper are: adap-org
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The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: chem-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: solv-int