Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cuplength estimates for periodic solutions of Hamiltonian particle-field
  systems   We consider a natural class of time-periodic infinite-dimensional nonlinear
Hamiltonian systems modelling the interaction of a classical mechanical system
of particles with a scalar wave field. When the field is defined on a space
torus $\mathbb{T}^d=\mathbb{R}^d/(2\pi\mathbb{Z})^d$ and the coordinates of the
particles are constrained to a submanifold $Q\subset\mathbb{T}^d$, we prove
that the number of $T$-periodic solutions of the coupled Hamiltonian
particle-field system is bounded from below by the $\mathbb{Z}_2$-cuplength of
the space of contractible loops in $Q$, provided that the square of the ratio
$T/2\pi$ of time period $T$ and space period $X=2\pi$ is a Diophantine
irrational number. The latter condition is necessary since for the
infinite-dimensional version of Gromov-Floer compactness as well as for the
$C^0$-bounds we need to deal with small divisors.

21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg