Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Symmetry reduction and periodic solutions in Hamiltonian Vlasov systems   In this paper, we discuss a general approach to find periodic solutions
bifurcating from equilibrium points of classical Vlasov systems. The main
access to the problem is chosen through the Hamiltonian representation of any
Vlasov system, firstly put forward by Fr\"ohlich, Knowles, and Schwarz, and
generalized more recently by the author. The method transforms the problem into
a setup of complex valued $\mathcal{L}^2$ functions with phase equivariant
Hamiltonian. Through Marsden-Weinstein symmetry reduction, the problem is
mapped on a Hamiltonian system on the quotient manifold
$\mathbb{S}^{\mathcal{L}^2}/\mathbb{S}^1$ which actually proves to be necessary
to close many trajectories of the dynamics. As a toy model to apply the method
we use the Harmonic Vlasov system, a non-relativistic Vlasov equation with
attractive harmonic two-body interaction potential. The simple structure of
this model allows to compute all of its solutions directly and therefore test
the benefits of the Hamiltonian formalism and symmetry reduction in Vlasov
systems.

30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn