ABSTRACT
In this chapter, the relationship between symmetries and first integrals for difference Hamiltonian equations is considered. These results are built upon those for the continuous canonical Hamiltonian equations
q˙i = ∂H
∂pi , p˙i = −∂H
∂qi , i = 1, . . . , n, (7.1)
considered in the Introduction. It was shown there that the continuous Hamiltonian equations can be obtained by the variational principle from action functionals. On the basis of Noether-type identities, there was developed a Noether-type theorem for the canonical Hamiltonian equations.
