Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the existence of infinitely many non-contractible periodic orbits of
  Hamiltonian diffeomorphisms of closed symplectic manifolds   We show that the presence of a non-contractible one-periodic orbit of a
Hamiltonian diffeomorphism of a connected closed symplectic manifold
$(M,\omega)$ implies the existence of infinitely many non-contractible simple
periodic orbits, provided that the symplectic form $\omega$ is aspherical and
the fundamental group $\pi_1(M)$ is either a virtually abelian group or an
$\mathrm{R}$-group. We also show that a similar statement holds for Hamiltonian
diffeomorphisms of closed monotone or negative monotone symplectic manifolds
under the same conditions on their fundamental groups. These results generalize
some works by Ginzburg and G\"urel. The proof uses the filtered Floer--Novikov
homology for non-contractible periodic orbits.

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The categories of this paper are: mtrl-th
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The categories of this paper are: eess
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
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The categories of this paper are: supr-con