Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dynamics and periodicity in a family of cluster maps   The dynamics of a 1-parameter family of cluster maps $\varphi_r$ associated
to mutation-periodic quivers in dimension 4, is studied in detail. The use of
presymplectic reduction leads to a globally periodic symplectic map, and this
enables us to reduce the problem to the study of maps belonging to a group of
symplectic birational maps of the plane which is isomorphic to
$SL(2,\mathbb{Z})\ltimes\mathbb{R}^2$. We conclude that there are three
different types of dynamical behaviour for $\varphi_r$ characterized by the
integer parameter values $r=1$, $r=2$ and $r>2$. For each type, the periodic
points, the structure and the asymptotic behaviour of the orbits are completely
described. A finer description of the dynamics is provided by using first
integrals.

37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
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
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom