Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dynamics of Actions of Automorphisms of Discrete Groups $G$ on Sub$_G$
  and Applications to Lattices in Lie Groups   For a discrete group $G$ and the compact space Sub$_G$ of (closed) subgroups
of $G$ endowed with the Chabauty topology, we study the dynamics of actions of
automorphisms of $G$ on Sub$_G$ in terms of distality and expansivity. We also
study the structure and properties of lattices $\Gamma$ in a connected Lie
group. In particular, we show that the unique maximal solvable normal subgroup
of $\Gamma$ is polycyclic and the corresponding quotient of $\Gamma$ is either
finite or admits a cofinite subgroup which is a lattice in a connected
semisimple Lie group with certain properties. We also show that Sub$^c_\Gamma$,
the set of cyclic subgroups of $\Gamma$, is closed in Sub$_\Gamma$. We prove
that an infinite discrete group $\Gamma$ which is either polycyclic or a
lattice in a connected Lie group, does not admit any automorphism which acts
expansively on Sub$^c_\Gamma$, while only the finite order automorphisms of
$\Gamma$ act distally on Sub$^c_\Gamma$. For an automorphism $T$ of a connected
Lie group $G$ and a $T$-invariant lattice $\Gamma$ in $G$, we compare the
behaviour of the actions of $T$ on Sub$_G$ and Sub$_\Gamma$ in terms of
distality. We put certain conditions on the structure of the Lie group $G$
under which we show that $T$ acts distally on Sub$_G$ if and only if it acts
distally on Sub$_\Gamma$. We construct counter examples to show that this does
not hold in general if the conditions on the Lie group are relaxed.

10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
3
The categories of this paper are: physics