Abstract
Hamiltonian dynamics, generalised in the usual way so that ideal (non-dissipative) models from fluid and plasma theory are included, has an interesting and useful adjoint structure. For linear theory this structure has several implications. For example, linearised Hamiltonian dynamics may be written as a Hermitian equation on Hilbert space provided the equilibrium state satisfy a certain stability criterion. Hamiltonian structure, Hermitian structure, exact dynamical invariants and variational principles are considered in this paper.
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