Canonical transformations for hyperhamiltonian dynamics in Euclidean spaces

We prove that in hyperhamiltonian dynamics, any local one-parameter group of canonical transformation is realized as the flow of a vector field related to the underlying hyperkahler structure, similarly to the case of standard Hamiltonian dynamics and the underlying symplectic structure. In this case the relevant class of vector fields is that of Dirac vector fields for the hyperkahler structure.