Normal forms for linear Hamiltonian vector fields commuting with the action of a compact Lie group

I. Melbourne, M. Dellnitz, Mathematical Proceedings of the Cambridge Philosophical Society (1993) 235–268.

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<jats:title>Abstract</jats:title><jats:p>We obtain normal forms for infinitesimally symplectic matrices (or linear Hamiltonian vector fields) that commute with the symplectic action of a compact Lie group of symmetries. In doing so we extend Williamson's theorem on normal forms when there is no symmetry present.</jats:p><jats:p>Using standard representation-theoretic results the symmetry can be factored out and we reduce to finding normal forms over a real division ring. There are three real division rings consisting of the real, complex and quaternionic numbers. Of these, only the real case is covered in Williamson's original work.</jats:p>
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Mathematical Proceedings of the Cambridge Philosophical Society
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235-268
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Melbourne I, Dellnitz M. Normal forms for linear Hamiltonian vector fields commuting with the action of a compact Lie group. Mathematical Proceedings of the Cambridge Philosophical Society. 1993:235-268. doi:10.1017/s0305004100071577
Melbourne, I., & Dellnitz, M. (1993). Normal forms for linear Hamiltonian vector fields commuting with the action of a compact Lie group. Mathematical Proceedings of the Cambridge Philosophical Society, 235–268. https://doi.org/10.1017/s0305004100071577
@article{Melbourne_Dellnitz_1993, title={Normal forms for linear Hamiltonian vector fields commuting with the action of a compact Lie group}, DOI={10.1017/s0305004100071577}, journal={Mathematical Proceedings of the Cambridge Philosophical Society}, author={Melbourne, Ian and Dellnitz, Michael}, year={1993}, pages={235–268} }
Melbourne, Ian, and Michael Dellnitz. “Normal Forms for Linear Hamiltonian Vector Fields Commuting with the Action of a Compact Lie Group.” Mathematical Proceedings of the Cambridge Philosophical Society, 1993, 235–68. https://doi.org/10.1017/s0305004100071577.
I. Melbourne and M. Dellnitz, “Normal forms for linear Hamiltonian vector fields commuting with the action of a compact Lie group,” Mathematical Proceedings of the Cambridge Philosophical Society, pp. 235–268, 1993.
Melbourne, Ian, and Michael Dellnitz. “Normal Forms for Linear Hamiltonian Vector Fields Commuting with the Action of a Compact Lie Group.” Mathematical Proceedings of the Cambridge Philosophical Society, 1993, pp. 235–68, doi:10.1017/s0305004100071577.

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