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.
Canonical transformations for hyperhamiltonian dynamics in Euclidean spaces / G. Gaeta, M.A. Rodríguez. - In: JOURNAL OF GEOMETRY AND PHYSICS. - ISSN 0393-0440. - 113(2017 Mar), pp. 38-52. [10.1016/j.geomphys.2016.08.013]
Canonical transformations for hyperhamiltonian dynamics in Euclidean spaces
G. Gaeta
;
2017
Abstract
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.
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