Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Nub of an Automorphism of a Totally Disconnected, Locally Compact
  Group   To any automorphism, $\alpha$, of a totally disconnected, locally compact
group, $G$, there is associated a compact, $\alpha$-stable subgroup of $G$,
here called the \emph{nub} of $\alpha$, on which the action of $\alpha$ is
topologically transitive. Topologically transitive actions of automorphisms of
compact groups have been studied extensively in topological dynamics and
results obtained transfer, via the nub, to the study of automorphisms of
general locally compact groups.
  A new proof that the contraction group of $\alpha$ is dense in the nub is
given, but it is seen that the two-sided contraction group need not be dense.
It is also shown that each pair $(G,\alpha)$, with $G$ compact and $\alpha$
topologically transitive, is an inverse limit of pairs that have `finite depth'
and that analogues of the Schreier Refinement and Jordan-H\"older Theorems hold
for pairs with finite depth.

9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat