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