Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Planar Hamiltonian systems: index theory and applications to the
  existence of subharmonics   We consider a planar Hamiltonian system of the type $Jz' = \nabla_z H(t,z)$,
where $H: \mathbb{R} \times \mathbb{R}^2 \to \mathbb{R}$ is a function periodic
in the time variable, such that $\nabla_z H(t,0) \equiv 0$ and $\nabla_z
H(t,z)$ is asymptotically linear for $\vert z \vert \to +\infty$. After
revisiting the index theory for linear planar Hamiltonian systems, by using the
Poincar\'e-Birkhoff fixed point theorem we prove that the above nonlinear
system has subharmonic solutions of any order $k$ large enough, whenever the
rotation numbers (or, equivalently, the mean Conley-Zehnder indices) of the
linearizations of the system at zero and at infinity are different.
Applications are given to the case of planar Hamiltonian systems coming from
second order scalar ODEs.

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The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat