Quadratic integrals of linear Hamiltonian systems. (English) Zbl 0541.34021
The momentum mapping of an autonomous, real linear Hamiltonian system is determined by its set of quadratic integrals. Such a system can be identified with an element of the real symplectic algebra and its quadratic integrals correspond to the centralizer of this element inside the symplectic algebra. In this paper, using a new set of normal forms for the elements of the real symplectic algebra, we compute their centralizers explicitly.
MSC:
| 34C20 | Transformation and reduction of ordinary differential equations and systems, normal forms |
| 70H05 | Hamilton’s equations |
| 34A30 | Linear ordinary differential equations and systems |
| 15A21 | Canonical forms, reductions, classification |
Keywords:
momentum mapping; real linear Hamiltonian system; quadratic integrals; real symplectic algebra; centralizersReferences:
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