Normal forms for linear Hamiltonian vector fields commuting with the action of a compact Lie group
1993 ◽
Vol 114
(2)
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pp. 235-268
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Keyword(s):
The Real
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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.
1993 ◽
Vol 114
(3)
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pp. 559-573
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2000 ◽
Vol 12
(12)
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pp. 1669-1688
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Keyword(s):
2003 ◽
Vol 44
(3)
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pp. 1173-1182
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1995 ◽
Vol 5
(2)
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pp. 153-170
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Keyword(s):