Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-Lagrangian Construction of Hamiltonian Structures   A method to construct Hamiltonian theories for systems of both ordinary and
partial differential equations is presented. The knowledge of a Lagrangian is
not at all necessary to achieve the result. The only ingredients required for
the construction are one solution of the symmetry (perturbation) equation and
one constant of the motion of the original system. It turns out that the
Poisson bracket structure for the dynamical variables is far from being
uniquely determined by the differential equations of motion. Examples in
classical mechanics as well as in field theory are presented.

16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
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The categories of this paper are: astro-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: acc-phys
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
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The categories of this paper are: quant-ph
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The categories of this paper are: q-fin