@article{16633,
  abstract     = {{<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       = {{Melbourne, Ian and Dellnitz, Michael}},
  issn         = {{0305-0041}},
  journal      = {{Mathematical Proceedings of the Cambridge Philosophical Society}},
  pages        = {{235--268}},
  title        = {{{Normal forms for linear Hamiltonian vector fields commuting with the action of a compact Lie group}}},
  doi          = {{10.1017/s0305004100071577}},
  year         = {{1993}},
}

@article{16634,
  author       = {{Melbourne, Ian and Dellnitz, Michael and Golubitsky, Martin}},
  issn         = {{0003-9527}},
  journal      = {{Archive for Rational Mechanics and Analysis}},
  pages        = {{75--98}},
  title        = {{{The structure of symmetric attractors}}},
  doi          = {{10.1007/bf00386369}},
  year         = {{1993}},
}

@article{17013,
  author       = {{Dellnitz, Michael}},
  journal      = {{Lectures in Applied Mathematics}},
  pages        = {{163--169}},
  title        = {{{The equivariant Darboux theorem}}},
  volume       = {{29}},
  year         = {{1993}},
}

@misc{51584,
  author       = {{Hilgert, Joachim}},
  booktitle    = {{JBer. DMV}},
  title        = {{{Corwin, L. und F.P. Greenleaf. Representations of Nilpotent Lie Groups and their Applications. (Cambridge University Press, 1990)}}},
  volume       = {{95}},
  year         = {{1993}},
}

@book{51496,
  author       = {{Hilgert, Joachim and Neeb, Karl-Hermann}},
  publisher    = {{Springer}},
  title        = {{{Lie Semigroups and their Applications}}},
  volume       = {{1552}},
  year         = {{1993}},
}

@article{40216,
  author       = {{Lasser, R. and Rösler, Margit}},
  issn         = {{0003-889X}},
  journal      = {{Archiv der Mathematik}},
  keywords     = {{General Mathematics}},
  number       = {{5}},
  pages        = {{459--463}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{A note on property (T) of orthogonal polynomials}}},
  doi          = {{10.1007/bf01202312}},
  volume       = {{60}},
  year         = {{1993}},
}

@inbook{16546,
  author       = {{Dellnitz, Michael and Golubitsky, Martin and Melbourne, Ian}},
  booktitle    = {{Bifurcation and Symmetry}},
  isbn         = {{9783034875387}},
  title        = {{{Mechanisms of Symmetry Creation}}},
  doi          = {{10.1007/978-3-0348-7536-3_9}},
  year         = {{1992}},
}

@inbook{16547,
  author       = {{Dellnitz, Michael and Marsden, Jerrold E. and Melbourne, Ian and Scheurle, Jürgen}},
  booktitle    = {{Bifurcation and Symmetry}},
  isbn         = {{9783034875387}},
  title        = {{{Generic Bifurcations of Pendula}}},
  doi          = {{10.1007/978-3-0348-7536-3_10}},
  year         = {{1992}},
}

@article{16548,
  author       = {{Dellnitz, M and Melbourne, I and Marsden, J E}},
  issn         = {{0951-7715}},
  journal      = {{Nonlinearity}},
  pages        = {{979--996}},
  title        = {{{Generic bifurcation of Hamiltonian vector fields with symmetry}}},
  doi          = {{10.1088/0951-7715/5/4/008}},
  year         = {{1992}},
}

@article{17012,
  author       = {{Dellnitz, Michael}},
  journal      = {{IMA Journal of Numerical Analysis}},
  number       = {{3}},
  pages        = {{429--455}},
  title        = {{{Computational bifurcation of periodic solutions in systems with symmetry}}},
  doi          = {{10.1093/imanum/12.3.429}},
  volume       = {{12}},
  year         = {{1992}},
}

@misc{51585,
  author       = {{Hilgert, Joachim}},
  booktitle    = {{JBer. DMV}},
  title        = {{{Fomenko, A.T. Symplectic Geometry (Gordon and Breach, 1988)}}},
  volume       = {{94}},
  year         = {{1992}},
}

@article{51442,
  author       = {{Hilgert, Joachim and Ólafsson, G.}},
  journal      = {{Japan. J. Math.}},
  pages        = {{213--290}},
  title        = {{{Analytic Extensions of Representations, the Solvable Case}}},
  volume       = {{18}},
  year         = {{1992}},
}

@article{51443,
  author       = {{Hilgert, Joachim}},
  journal      = {{Math. Zeitschrift}},
  pages        = {{463--466}},
  title        = {{{Controllability on Real Reductive Groups}}},
  volume       = {{209}},
  year         = {{1992}},
}

@phdthesis{54832,
  author       = {{Rösler, Margit}},
  title        = {{{Durch orthogonale trigonometrische Systeme auf dem Einheitskreis induzierte Faltunsstrukturen auf Z}}},
  year         = {{1992}},
}

@misc{51588,
  author       = {{Hilgert, Joachim}},
  booktitle    = {{JBer. DMV}},
  number       = {{4}},
  title        = {{{Varadarajan, V.S. An Introduction to Harmonic Analysis on Semisimple Lie Groups (Cambridge University Press, 1989)}}},
  volume       = {{94}},
  year         = {{1991}},
}

@misc{51589,
  author       = {{Hilgert, Joachim}},
  booktitle    = {{JBer. DMV}},
  number       = {{2}},
  title        = {{{Terras, A. Harmonic Analysis on Symmetric Spaces I and II (Springer, New York, 1985 und 1988)}}},
  volume       = {{93}},
  year         = {{1991}},
}

@article{51445,
  author       = {{Hilgert, Joachim and Ólafsson, G. and Orsted, B.}},
  journal      = {{J. reine und angew. Math.}},
  pages        = {{189--218}},
  title        = {{{Hardy Spaces on Affine Symmetric Spaces}}},
  volume       = {{415}},
  year         = {{1991}},
}

@inbook{51483,
  author       = {{Hilgert, Joachim}},
  booktitle    = {{Jahrbuch der Gödel Gesellschaft}},
  editor       = {{Hilgert, Joachim}},
  title        = {{{Group Theoretical Aspects of Gödels Model}}},
  year         = {{1991}},
}

@article{51444,
  author       = {{Hilgert, Joachim}},
  journal      = {{Rocky Mount. J. Math.}},
  pages        = {{865--878}},
  title        = {{{Infinitesimally Generated Subsemigroups of Motion Groups}}},
  volume       = {{21}},
  year         = {{1991}},
}

@misc{51586,
  author       = {{Hilgert, Joachim}},
  booktitle    = {{Zentralblatt}},
  title        = {{{Onishchik, A.L., und E.B. Vinberg. Lie Groups and Algebraic Groups (Springer, New York, 1990)}}},
  volume       = {{722}},
  year         = {{1991}},
}