{"publication_status":"published","language":[{"iso":"eng"}],"type":"journal_article","date_updated":"2022-01-06T06:52:53Z","publication":"Mathematical Proceedings of the Cambridge Philosophical Society","page":"235-268","doi":"10.1017/s0305004100071577","abstract":[{"lang":"eng","text":"<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>"}],"author":[{"last_name":"Melbourne","full_name":"Melbourne, Ian","first_name":"Ian"},{"first_name":"Michael","full_name":"Dellnitz, Michael","last_name":"Dellnitz"}],"year":"1993","status":"public","date_created":"2020-04-16T08:31:40Z","user_id":"15701","citation":{"ieee":"I. Melbourne and M. Dellnitz, “Normal forms for linear Hamiltonian vector fields commuting with the action of a compact Lie group,” <i>Mathematical Proceedings of the Cambridge Philosophical Society</i>, pp. 235–268, 1993.","mla":"Melbourne, Ian, and Michael Dellnitz. “Normal Forms for Linear Hamiltonian Vector Fields Commuting with the Action of a Compact Lie Group.” <i>Mathematical Proceedings of the Cambridge Philosophical Society</i>, 1993, pp. 235–68, doi:<a href=\"https://doi.org/10.1017/s0305004100071577\">10.1017/s0305004100071577</a>.","ama":"Melbourne I, Dellnitz M. Normal forms for linear Hamiltonian vector fields commuting with the action of a compact Lie group. <i>Mathematical Proceedings of the Cambridge Philosophical Society</i>. 1993:235-268. doi:<a href=\"https://doi.org/10.1017/s0305004100071577\">10.1017/s0305004100071577</a>","apa":"Melbourne, I., &#38; Dellnitz, M. (1993). Normal forms for linear Hamiltonian vector fields commuting with the action of a compact Lie group. <i>Mathematical Proceedings of the Cambridge Philosophical Society</i>, 235–268. <a href=\"https://doi.org/10.1017/s0305004100071577\">https://doi.org/10.1017/s0305004100071577</a>","bibtex":"@article{Melbourne_Dellnitz_1993, title={Normal forms for linear Hamiltonian vector fields commuting with the action of a compact Lie group}, DOI={<a href=\"https://doi.org/10.1017/s0305004100071577\">10.1017/s0305004100071577</a>}, 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.","chicago":"Melbourne, Ian, and Michael Dellnitz. “Normal Forms for Linear Hamiltonian Vector Fields Commuting with the Action of a Compact Lie Group.” <i>Mathematical Proceedings of the Cambridge Philosophical Society</i>, 1993, 235–68. <a href=\"https://doi.org/10.1017/s0305004100071577\">https://doi.org/10.1017/s0305004100071577</a>."},"_id":"16633","title":"Normal forms for linear Hamiltonian vector fields commuting with the action of a compact Lie group","department":[{"_id":"101"}],"publication_identifier":{"issn":["0305-0041","1469-8064"]}}