Distinguished Hamiltonian theorem for homogeneous symplectic manifolds (Q1182285)

A diffeomorphism \(\phi\) of a symplectic manifold \((M,\omega)\) is said to be canonoid with respect to a locally Hamiltonian vector field \(X\) if the field \(\phi_ *X\) is also locally Hamiltonian. \(\phi\) is called a conformal symplectomorphism if \(\phi_ *X\) is a constant scalar multiple of \(\omega\); then \(\phi\) is canonoid with respect to all locally Hamiltonian vector fields \(X\). A set \(S\) of locally Hamiltonian vector fields is a sufficiency set if every diffeomorphism which is canonoid for all \(X\in S\) is a conformal symplectomorphism. In this paper various sufficiency sets are found, generalizing the ``quadratic Hamiltonian theorem'' of Currie and Saletan. Particular emphasis is placed on infinite-dimensional examples.