Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Skew-product dynamical systems for crossed product $C^*$-algebras and
  their ergodic properties   Starting from a discrete $C^*$-dynamical system $(\mathfrak{A}, \theta,
\omega_o)$, we define and study most of the main ergodic properties of the
crossed product $C^*$-dynamical system $(\mathfrak{A}\rtimes_\alpha\mathbb{Z},
\Phi_{\theta, u},\om_o\circ E)$,
$E:\mathfrak{A}\rtimes_\alpha\mathbb{Z}\rightarrow\ga$ being the canonical
conditional expectation of $\mathfrak{A}\rtimes_\alpha\mathbb{Z}$ onto
$\mathfrak{A}$, provided $\a\in\aut(\ga)$ commute with the $*$-automorphism
$\th$ up tu a unitary $u\in\ga$. Here, $\Phi_{\theta,
u}\in\aut(\mathfrak{A}\rtimes_\alpha\mathbb{Z})$ can be considered as the fully
noncommutative generalisation of the celebrated skew-product defined by H.
Anzai for the product of two tori in the classical case.

12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess