%0 Journal Article
%T Symmetry and quaternionic integrable systems
%A Giuseppe Gaeta
%A Miguel Angel Rodriguez
%J Physics
%D 2015
%I arXiv
%R 10.1016/j.geomphys.2014.05.019
%X Given a hyperkahler manifold M, the hyperkahler structure defines a triple of symplectic structures on M; with these, a triple of Hamiltonians defines a so called hyperhamiltonian dynamical system on M. These systems are integrable when can be mapped to a system of quaternionic oscillators. We discuss the symmetry of integrable hyperhamiltonian systems, i.e. quaternionic oscillators; and conversely how these symmetries characterize, at least in the Euclidean case, integrable hyperhamiltonian systems.
%U http://arxiv.org/abs/1512.03490v1