Abstract
In this note we consider the relation between symmetries and first integrals for discrete Hamiltonian equations. We observe that canonical Hamiltonian equations can be obtained by variational principle from an action functional. A discrete analog of this property is used to define discrete Hamiltonian equations. Discrete Noether’s theorem links symmetries and first integrals of discrete Hamiltonian equations. This relation can be used to conserve structural properties of Hamiltonian equations in numerical implementation.
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