Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Invariance and first integrals of continuous and discrete Hamiltonian
  equations   In this paper we consider the relation between symmetries and first integrals
for both continuous canonical Hamiltonian equations and discrete Hamiltonian
equations. We observe that canonical Hamiltonian equations can be obtained by
variational principle from an action functional and consider invariance
properties of this functional as it is done in Lagrangian formalism. We rewrite
the well--known Noether's identity in terms of the Hamiltonian function and
symmetry operators. This approach, based on symmetries of the Hamiltonian
action, provides a simple and clear way to construct first integrals of
Hamiltonian equations without integration. A discrete analog of this identity
is developed. It leads to a relation between symmetries and first integrals for
discrete Hamiltonian equations that can be used to conserve structural
properties of Hamiltonian equations in numerical implementation. The results
are illustrated by a number of examples for both continuous and discrete
Hamiltonian equations.

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The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
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The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
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The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int