Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dynamics of $\mathcal B$-free sets: a view through the window   Let $\mathcal B$ be an infinite subset of $\{1,2,\dots\}$. We characterize
arithmetic and dynamical properties of the $\mathcal B$-free set $\mathcal
F_{\mathcal B}$ through group theoretical, topological and measure theoretic
properties of a set $W$ (called the window) associated with $\mathcal B$. This
point of view stems from the interpretation of the set $\mathcal F_{\mathcal
B}$ as a weak model set. Our main results are: $\mathcal B$ is taut if and only
if the window is Haar regular; the dynamical system associated to $\mathcal
F_{\mathcal B}$ is a Toeplitz system if and only if the window is topologically
regular; the dynamical system associated to $\mathcal F_{\mathcal B}$ is
proximal if and only if the window has empty interior; and the dynamical system
associated to $\mathcal F_{\mathcal B}$ has the "na\"ively expected" maximal
equicontinuous factor if and only if the interior of the window is aperiodic.

35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph