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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>"}],"user_id":"15701","department":[{"_id":"101"}],"_id":"16633","language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["0305-0041","1469-8064"]},"citation":{"short":"I. Melbourne, M. 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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>"},"page":"235-268","year":"1993","date_created":"2020-04-16T08:31:40Z","author":[{"full_name":"Melbourne, Ian","last_name":"Melbourne","first_name":"Ian"},{"first_name":"Michael","last_name":"Dellnitz","full_name":"Dellnitz, Michael"}],"date_updated":"2022-01-06T06:52:53Z","doi":"10.1017/s0305004100071577","title":"Normal forms for linear Hamiltonian vector fields commuting with the action of a compact Lie group"},{"publication_identifier":{"issn":["0003-9527","1432-0673"]},"publication_status":"published","page":"75-98","citation":{"chicago":"Melbourne, Ian, Michael Dellnitz, and Martin Golubitsky. “The Structure of Symmetric Attractors.” <i>Archive for Rational Mechanics and Analysis</i>, 1993, 75–98. <a href=\"https://doi.org/10.1007/bf00386369\">https://doi.org/10.1007/bf00386369</a>.","ieee":"I. 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