[{"year":"1993","department":[{"_id":"101"}],"page":"235-268","citation":{"ieee":"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.","chicago":"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.","bibtex":"@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} }","ama":"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","mla":"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.","apa":"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","short":"I. Melbourne, M. Dellnitz, Mathematical Proceedings of the Cambridge Philosophical Society (1993) 235–268."},"user_id":"15701","date_created":"2020-04-16T08:31:40Z","status":"public","type":"journal_article","_id":"16633","title":"Normal forms for linear Hamiltonian vector fields commuting with the action of a compact Lie group","publication_status":"published","abstract":[{"text":"AbstractWe 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.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.","lang":"eng"}],"publication_identifier":{"issn":["0305-0041","1469-8064"]},"date_updated":"2020-05-19T07:15:35Z","publication":"Mathematical Proceedings of the Cambridge Philosophical Society","language":[{"iso":"eng"}],"author":[{"full_name":"Melbourne, Ian","last_name":"Melbourne","first_name":"Ian"},{"first_name":"Michael","last_name":"Dellnitz","full_name":"Dellnitz, Michael"}],"doi":"10.1017/s0305004100071577"}]