Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Conditional mean dimension   We introduce some notions of conditional mean dimension for a factor map
between two topological dynamical systems and discuss their properties. With
the help of these notions, we obtain an inequality to estimate the mean
dimension of an extension system. The conditional mean dimension for
$G$-extensions are computed. We also exhibit some applications in the dynamical
embedding problems.

33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph