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.
Symmetry and quaternionic integrable systems / G. Gaeta, M.A. Rodriguez. - In: JOURNAL OF GEOMETRY AND PHYSICS. - ISSN 0393-0440. - 87(2015 Jan), pp. 134-148. [10.1016/j.geomphys.2014.05.019]
Symmetry and quaternionic integrable systems
G. GaetaPrimo
;
2015
Abstract
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.File | Dimensione | Formato | |
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