---
_id: '16633'
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:
- first_name: Ian
  full_name: Melbourne, Ian
  last_name: Melbourne
- first_name: Michael
  full_name: Dellnitz, Michael
  last_name: Dellnitz
citation:
  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} }'
  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>.
  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>.
  short: I. Melbourne, M. Dellnitz, Mathematical Proceedings of the Cambridge Philosophical
    Society (1993) 235–268.
date_created: 2020-04-16T08:31:40Z
date_updated: 2022-01-06T06:52:53Z
department:
- _id: '101'
doi: 10.1017/s0305004100071577
language:
- iso: eng
page: 235-268
publication: Mathematical Proceedings of the Cambridge Philosophical Society
publication_identifier:
  issn:
  - 0305-0041
  - 1469-8064
publication_status: published
status: public
title: Normal forms for linear Hamiltonian vector fields commuting with the action
  of a compact Lie group
type: journal_article
user_id: '15701'
year: '1993'
...
---
_id: '16634'
author:
- first_name: Ian
  full_name: Melbourne, Ian
  last_name: Melbourne
- first_name: Michael
  full_name: Dellnitz, Michael
  last_name: Dellnitz
- first_name: Martin
  full_name: Golubitsky, Martin
  last_name: Golubitsky
citation:
  ama: Melbourne I, Dellnitz M, Golubitsky M. The structure of symmetric attractors.
    <i>Archive for Rational Mechanics and Analysis</i>. 1993:75-98. doi:<a href="https://doi.org/10.1007/bf00386369">10.1007/bf00386369</a>
  apa: Melbourne, I., Dellnitz, M., &#38; Golubitsky, M. (1993). The structure of
    symmetric attractors. <i>Archive for Rational Mechanics and Analysis</i>, 75–98.
    <a href="https://doi.org/10.1007/bf00386369">https://doi.org/10.1007/bf00386369</a>
  bibtex: '@article{Melbourne_Dellnitz_Golubitsky_1993, title={The structure of symmetric
    attractors}, DOI={<a href="https://doi.org/10.1007/bf00386369">10.1007/bf00386369</a>},
    journal={Archive for Rational Mechanics and Analysis}, author={Melbourne, Ian
    and Dellnitz, Michael and Golubitsky, Martin}, year={1993}, pages={75–98} }'
  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. Melbourne, M. Dellnitz, and M. Golubitsky, “The structure of symmetric
    attractors,” <i>Archive for Rational Mechanics and Analysis</i>, pp. 75–98, 1993.
  mla: Melbourne, Ian, et al. “The Structure of Symmetric Attractors.” <i>Archive
    for Rational Mechanics and Analysis</i>, 1993, pp. 75–98, doi:<a href="https://doi.org/10.1007/bf00386369">10.1007/bf00386369</a>.
  short: I. Melbourne, M. Dellnitz, M. Golubitsky, Archive for Rational Mechanics
    and Analysis (1993) 75–98.
date_created: 2020-04-16T08:32:44Z
date_updated: 2022-01-06T06:52:53Z
department:
- _id: '101'
doi: 10.1007/bf00386369
language:
- iso: eng
page: 75-98
publication: Archive for Rational Mechanics and Analysis
publication_identifier:
  issn:
  - 0003-9527
  - 1432-0673
publication_status: published
status: public
title: The structure of symmetric attractors
type: journal_article
user_id: '15701'
year: '1993'
...
---
_id: '17013'
author:
- first_name: Michael
  full_name: Dellnitz, Michael
  last_name: Dellnitz
citation:
  ama: Dellnitz M. The equivariant Darboux theorem. <i>Lectures in Applied Mathematics</i>.
    1993;29:163-169.
  apa: Dellnitz, M. (1993). The equivariant Darboux theorem. <i>Lectures in Applied
    Mathematics</i>, <i>29</i>, 163–169.
  bibtex: '@article{Dellnitz_1993, title={The equivariant Darboux theorem}, volume={29},
    journal={Lectures in Applied Mathematics}, author={Dellnitz, Michael}, year={1993},
    pages={163–169} }'
  chicago: 'Dellnitz, Michael. “The Equivariant Darboux Theorem.” <i>Lectures in Applied
    Mathematics</i> 29 (1993): 163–69.'
  ieee: M. Dellnitz, “The equivariant Darboux theorem,” <i>Lectures in Applied Mathematics</i>,
    vol. 29, pp. 163–169, 1993.
  mla: Dellnitz, Michael. “The Equivariant Darboux Theorem.” <i>Lectures in Applied
    Mathematics</i>, vol. 29, 1993, pp. 163–69.
  short: M. Dellnitz, Lectures in Applied Mathematics 29 (1993) 163–169.
date_created: 2020-05-19T09:04:09Z
date_updated: 2022-01-06T06:53:02Z
department:
- _id: '101'
intvolume: '        29'
language:
- iso: eng
page: 163-169
publication: Lectures in Applied Mathematics
status: public
title: The equivariant Darboux theorem
type: journal_article
user_id: '32643'
volume: 29
year: '1993'
...
---
_id: '51584'
author:
- first_name: Joachim
  full_name: Hilgert, Joachim
  id: '220'
  last_name: Hilgert
citation:
  ama: Hilgert J. Corwin, L. und F.P. Greenleaf. Representations of Nilpotent Lie
    Groups and their Applications. (Cambridge University Press, 1990). <i>JBer DMV</i>.
    1993;95.
  apa: Hilgert, J. (1993). Corwin, L. und F.P. Greenleaf. Representations of Nilpotent
    Lie Groups and their Applications. (Cambridge University Press, 1990). In <i>JBer.
    DMV</i> (Vol. 95).
  bibtex: '@article{Hilgert_1993, title={Corwin, L. und F.P. Greenleaf. Representations
    of Nilpotent Lie Groups and their Applications. (Cambridge University Press, 1990)},
    volume={95}, journal={JBer. DMV}, author={Hilgert, Joachim}, year={1993} }'
  chicago: Hilgert, Joachim. “Corwin, L. Und F.P. Greenleaf. Representations of Nilpotent
    Lie Groups and Their Applications. (Cambridge University Press, 1990).” <i>JBer.
    DMV</i>, 1993.
  ieee: J. Hilgert, “Corwin, L. und F.P. Greenleaf. Representations of Nilpotent Lie
    Groups and their Applications. (Cambridge University Press, 1990),” <i>JBer. DMV</i>,
    vol. 95. 1993.
  mla: Hilgert, Joachim. “Corwin, L. Und F.P. Greenleaf. Representations of Nilpotent
    Lie Groups and Their Applications. (Cambridge University Press, 1990).” <i>JBer.
    DMV</i>, vol. 95, 1993.
  short: J. Hilgert, JBer. DMV 95 (1993).
date_created: 2024-02-20T12:24:27Z
date_updated: 2024-02-20T13:35:37Z
department:
- _id: '91'
extern: '1'
intvolume: '        95'
language:
- iso: eng
publication: JBer. DMV
publication_status: published
status: public
title: Corwin, L. und F.P. Greenleaf. Representations of Nilpotent Lie Groups and
  their Applications. (Cambridge University Press, 1990)
type: review
user_id: '49063'
volume: 95
year: '1993'
...
---
_id: '51496'
author:
- first_name: Joachim
  full_name: Hilgert, Joachim
  id: '220'
  last_name: Hilgert
- first_name: Karl-Hermann
  full_name: Neeb, Karl-Hermann
  last_name: Neeb
citation:
  ama: Hilgert J, Neeb K-H. <i>Lie Semigroups and Their Applications</i>. Vol 1552.
    Springer; 1993.
  apa: Hilgert, J., &#38; Neeb, K.-H. (1993). <i>Lie Semigroups and their Applications</i>
    (Vol. 1552). Springer.
  bibtex: '@book{Hilgert_Neeb_1993, series={LNM }, title={Lie Semigroups and their
    Applications}, volume={1552}, publisher={Springer}, author={Hilgert, Joachim and
    Neeb, Karl-Hermann}, year={1993}, collection={LNM } }'
  chicago: Hilgert, Joachim, and Karl-Hermann Neeb. <i>Lie Semigroups and Their Applications</i>.
    Vol. 1552. LNM . Springer, 1993.
  ieee: J. Hilgert and K.-H. Neeb, <i>Lie Semigroups and their Applications</i>, vol.
    1552. Springer, 1993.
  mla: Hilgert, Joachim, and Karl-Hermann Neeb. <i>Lie Semigroups and Their Applications</i>.
    Springer, 1993.
  short: J. Hilgert, K.-H. Neeb, Lie Semigroups and Their Applications, Springer,
    1993.
date_created: 2024-02-19T10:26:09Z
date_updated: 2024-08-08T08:19:14Z
department:
- _id: '91'
extern: '1'
intvolume: '      1552'
language:
- iso: eng
main_file_link:
- url: https://link.springer.com/book/10.1007/BFb0084640
publication_status: published
publisher: Springer
series_title: 'LNM '
status: public
title: Lie Semigroups and their Applications
type: book
user_id: '220'
volume: 1552
year: '1993'
...
---
_id: '40216'
author:
- first_name: R.
  full_name: Lasser, R.
  last_name: Lasser
- first_name: Margit
  full_name: Rösler, Margit
  id: '37390'
  last_name: Rösler
citation:
  ama: Lasser R, Rösler M. A note on property (T) of orthogonal polynomials. <i>Archiv
    der Mathematik</i>. 1993;60(5):459-463. doi:<a href="https://doi.org/10.1007/bf01202312">10.1007/bf01202312</a>
  apa: Lasser, R., &#38; Rösler, M. (1993). A note on property (T) of orthogonal polynomials.
    <i>Archiv Der Mathematik</i>, <i>60</i>(5), 459–463. <a href="https://doi.org/10.1007/bf01202312">https://doi.org/10.1007/bf01202312</a>
  bibtex: '@article{Lasser_Rösler_1993, title={A note on property (T) of orthogonal
    polynomials}, volume={60}, DOI={<a href="https://doi.org/10.1007/bf01202312">10.1007/bf01202312</a>},
    number={5}, journal={Archiv der Mathematik}, publisher={Springer Science and Business
    Media LLC}, author={Lasser, R. and Rösler, Margit}, year={1993}, pages={459–463}
    }'
  chicago: 'Lasser, R., and Margit Rösler. “A Note on Property (T) of Orthogonal Polynomials.”
    <i>Archiv Der Mathematik</i> 60, no. 5 (1993): 459–63. <a href="https://doi.org/10.1007/bf01202312">https://doi.org/10.1007/bf01202312</a>.'
  ieee: 'R. Lasser and M. Rösler, “A note on property (T) of orthogonal polynomials,”
    <i>Archiv der Mathematik</i>, vol. 60, no. 5, pp. 459–463, 1993, doi: <a href="https://doi.org/10.1007/bf01202312">10.1007/bf01202312</a>.'
  mla: Lasser, R., and Margit Rösler. “A Note on Property (T) of Orthogonal Polynomials.”
    <i>Archiv Der Mathematik</i>, vol. 60, no. 5, Springer Science and Business Media
    LLC, 1993, pp. 459–63, doi:<a href="https://doi.org/10.1007/bf01202312">10.1007/bf01202312</a>.
  short: R. Lasser, M. Rösler, Archiv Der Mathematik 60 (1993) 459–463.
date_created: 2023-01-26T09:05:30Z
date_updated: 2023-01-26T17:33:57Z
department:
- _id: '555'
doi: 10.1007/bf01202312
extern: '1'
intvolume: '        60'
issue: '5'
keyword:
- General Mathematics
language:
- iso: eng
page: 459-463
publication: Archiv der Mathematik
publication_identifier:
  issn:
  - 0003-889X
  - 1420-8938
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: A note on property (T) of orthogonal polynomials
type: journal_article
user_id: '37390'
volume: 60
year: '1993'
...
---
_id: '16546'
author:
- first_name: Michael
  full_name: Dellnitz, Michael
  last_name: Dellnitz
- first_name: Martin
  full_name: Golubitsky, Martin
  last_name: Golubitsky
- first_name: Ian
  full_name: Melbourne, Ian
  last_name: Melbourne
citation:
  ama: 'Dellnitz M, Golubitsky M, Melbourne I. Mechanisms of Symmetry Creation. In:
    <i>Bifurcation and Symmetry</i>. Basel; 1992. doi:<a href="https://doi.org/10.1007/978-3-0348-7536-3_9">10.1007/978-3-0348-7536-3_9</a>'
  apa: Dellnitz, M., Golubitsky, M., &#38; Melbourne, I. (1992). Mechanisms of Symmetry
    Creation. In <i>Bifurcation and Symmetry</i>. Basel. <a href="https://doi.org/10.1007/978-3-0348-7536-3_9">https://doi.org/10.1007/978-3-0348-7536-3_9</a>
  bibtex: '@inbook{Dellnitz_Golubitsky_Melbourne_1992, place={Basel}, title={Mechanisms
    of Symmetry Creation}, DOI={<a href="https://doi.org/10.1007/978-3-0348-7536-3_9">10.1007/978-3-0348-7536-3_9</a>},
    booktitle={Bifurcation and Symmetry}, author={Dellnitz, Michael and Golubitsky,
    Martin and Melbourne, Ian}, year={1992} }'
  chicago: Dellnitz, Michael, Martin Golubitsky, and Ian Melbourne. “Mechanisms of
    Symmetry Creation.” In <i>Bifurcation and Symmetry</i>. Basel, 1992. <a href="https://doi.org/10.1007/978-3-0348-7536-3_9">https://doi.org/10.1007/978-3-0348-7536-3_9</a>.
  ieee: M. Dellnitz, M. Golubitsky, and I. Melbourne, “Mechanisms of Symmetry Creation,”
    in <i>Bifurcation and Symmetry</i>, Basel, 1992.
  mla: Dellnitz, Michael, et al. “Mechanisms of Symmetry Creation.” <i>Bifurcation
    and Symmetry</i>, 1992, doi:<a href="https://doi.org/10.1007/978-3-0348-7536-3_9">10.1007/978-3-0348-7536-3_9</a>.
  short: 'M. Dellnitz, M. Golubitsky, I. Melbourne, in: Bifurcation and Symmetry,
    Basel, 1992.'
date_created: 2020-04-15T08:56:42Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1007/978-3-0348-7536-3_9
language:
- iso: eng
place: Basel
publication: Bifurcation and Symmetry
publication_identifier:
  isbn:
  - '9783034875387'
  - '9783034875363'
publication_status: published
status: public
title: Mechanisms of Symmetry Creation
type: book_chapter
user_id: '15701'
year: '1992'
...
---
_id: '16547'
author:
- first_name: Michael
  full_name: Dellnitz, Michael
  last_name: Dellnitz
- first_name: Jerrold E.
  full_name: Marsden, Jerrold E.
  last_name: Marsden
- first_name: Ian
  full_name: Melbourne, Ian
  last_name: Melbourne
- first_name: Jürgen
  full_name: Scheurle, Jürgen
  last_name: Scheurle
citation:
  ama: 'Dellnitz M, Marsden JE, Melbourne I, Scheurle J. Generic Bifurcations of Pendula.
    In: <i>Bifurcation and Symmetry</i>. Basel; 1992. doi:<a href="https://doi.org/10.1007/978-3-0348-7536-3_10">10.1007/978-3-0348-7536-3_10</a>'
  apa: Dellnitz, M., Marsden, J. E., Melbourne, I., &#38; Scheurle, J. (1992). Generic
    Bifurcations of Pendula. In <i>Bifurcation and Symmetry</i>. Basel. <a href="https://doi.org/10.1007/978-3-0348-7536-3_10">https://doi.org/10.1007/978-3-0348-7536-3_10</a>
  bibtex: '@inbook{Dellnitz_Marsden_Melbourne_Scheurle_1992, place={Basel}, title={Generic
    Bifurcations of Pendula}, DOI={<a href="https://doi.org/10.1007/978-3-0348-7536-3_10">10.1007/978-3-0348-7536-3_10</a>},
    booktitle={Bifurcation and Symmetry}, author={Dellnitz, Michael and Marsden, Jerrold
    E. and Melbourne, Ian and Scheurle, Jürgen}, year={1992} }'
  chicago: Dellnitz, Michael, Jerrold E. Marsden, Ian Melbourne, and Jürgen Scheurle.
    “Generic Bifurcations of Pendula.” In <i>Bifurcation and Symmetry</i>. Basel,
    1992. <a href="https://doi.org/10.1007/978-3-0348-7536-3_10">https://doi.org/10.1007/978-3-0348-7536-3_10</a>.
  ieee: M. Dellnitz, J. E. Marsden, I. Melbourne, and J. Scheurle, “Generic Bifurcations
    of Pendula,” in <i>Bifurcation and Symmetry</i>, Basel, 1992.
  mla: Dellnitz, Michael, et al. “Generic Bifurcations of Pendula.” <i>Bifurcation
    and Symmetry</i>, 1992, doi:<a href="https://doi.org/10.1007/978-3-0348-7536-3_10">10.1007/978-3-0348-7536-3_10</a>.
  short: 'M. Dellnitz, J.E. Marsden, I. Melbourne, J. Scheurle, in: Bifurcation and
    Symmetry, Basel, 1992.'
date_created: 2020-04-15T08:58:01Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1007/978-3-0348-7536-3_10
language:
- iso: eng
place: Basel
publication: Bifurcation and Symmetry
publication_identifier:
  isbn:
  - '9783034875387'
  - '9783034875363'
publication_status: published
status: public
title: Generic Bifurcations of Pendula
type: book_chapter
user_id: '15701'
year: '1992'
...
---
_id: '16548'
author:
- first_name: M
  full_name: Dellnitz, M
  last_name: Dellnitz
- first_name: I
  full_name: Melbourne, I
  last_name: Melbourne
- first_name: J E
  full_name: Marsden, J E
  last_name: Marsden
citation:
  ama: Dellnitz M, Melbourne I, Marsden JE. Generic bifurcation of Hamiltonian vector
    fields with symmetry. <i>Nonlinearity</i>. 1992:979-996. doi:<a href="https://doi.org/10.1088/0951-7715/5/4/008">10.1088/0951-7715/5/4/008</a>
  apa: Dellnitz, M., Melbourne, I., &#38; Marsden, J. E. (1992). Generic bifurcation
    of Hamiltonian vector fields with symmetry. <i>Nonlinearity</i>, 979–996. <a href="https://doi.org/10.1088/0951-7715/5/4/008">https://doi.org/10.1088/0951-7715/5/4/008</a>
  bibtex: '@article{Dellnitz_Melbourne_Marsden_1992, title={Generic bifurcation of
    Hamiltonian vector fields with symmetry}, DOI={<a href="https://doi.org/10.1088/0951-7715/5/4/008">10.1088/0951-7715/5/4/008</a>},
    journal={Nonlinearity}, author={Dellnitz, M and Melbourne, I and Marsden, J E},
    year={1992}, pages={979–996} }'
  chicago: Dellnitz, M, I Melbourne, and J E Marsden. “Generic Bifurcation of Hamiltonian
    Vector Fields with Symmetry.” <i>Nonlinearity</i>, 1992, 979–96. <a href="https://doi.org/10.1088/0951-7715/5/4/008">https://doi.org/10.1088/0951-7715/5/4/008</a>.
  ieee: M. Dellnitz, I. Melbourne, and J. E. Marsden, “Generic bifurcation of Hamiltonian
    vector fields with symmetry,” <i>Nonlinearity</i>, pp. 979–996, 1992.
  mla: Dellnitz, M., et al. “Generic Bifurcation of Hamiltonian Vector Fields with
    Symmetry.” <i>Nonlinearity</i>, 1992, pp. 979–96, doi:<a href="https://doi.org/10.1088/0951-7715/5/4/008">10.1088/0951-7715/5/4/008</a>.
  short: M. Dellnitz, I. Melbourne, J.E. Marsden, Nonlinearity (1992) 979–996.
date_created: 2020-04-15T08:59:25Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1088/0951-7715/5/4/008
language:
- iso: eng
page: 979-996
publication: Nonlinearity
publication_identifier:
  issn:
  - 0951-7715
  - 1361-6544
publication_status: published
status: public
title: Generic bifurcation of Hamiltonian vector fields with symmetry
type: journal_article
user_id: '15701'
year: '1992'
...
---
_id: '17012'
author:
- first_name: Michael
  full_name: Dellnitz, Michael
  last_name: Dellnitz
citation:
  ama: Dellnitz M. Computational bifurcation of periodic solutions in systems with
    symmetry. <i>IMA Journal of Numerical Analysis</i>. 1992;12(3):429-455. doi:<a
    href="https://doi.org/10.1093/imanum/12.3.429">10.1093/imanum/12.3.429</a>
  apa: Dellnitz, M. (1992). Computational bifurcation of periodic solutions in systems
    with symmetry. <i>IMA Journal of Numerical Analysis</i>, <i>12</i>(3), 429–455.
    <a href="https://doi.org/10.1093/imanum/12.3.429">https://doi.org/10.1093/imanum/12.3.429</a>
  bibtex: '@article{Dellnitz_1992, title={Computational bifurcation of periodic solutions
    in systems with symmetry}, volume={12}, DOI={<a href="https://doi.org/10.1093/imanum/12.3.429">10.1093/imanum/12.3.429</a>},
    number={3}, journal={IMA Journal of Numerical Analysis}, author={Dellnitz, Michael},
    year={1992}, pages={429–455} }'
  chicago: 'Dellnitz, Michael. “Computational Bifurcation of Periodic Solutions in
    Systems with Symmetry.” <i>IMA Journal of Numerical Analysis</i> 12, no. 3 (1992):
    429–55. <a href="https://doi.org/10.1093/imanum/12.3.429">https://doi.org/10.1093/imanum/12.3.429</a>.'
  ieee: M. Dellnitz, “Computational bifurcation of periodic solutions in systems with
    symmetry,” <i>IMA Journal of Numerical Analysis</i>, vol. 12, no. 3, pp. 429–455,
    1992.
  mla: Dellnitz, Michael. “Computational Bifurcation of Periodic Solutions in Systems
    with Symmetry.” <i>IMA Journal of Numerical Analysis</i>, vol. 12, no. 3, 1992,
    pp. 429–55, doi:<a href="https://doi.org/10.1093/imanum/12.3.429">10.1093/imanum/12.3.429</a>.
  short: M. Dellnitz, IMA Journal of Numerical Analysis 12 (1992) 429–455.
date_created: 2020-05-19T08:53:14Z
date_updated: 2022-01-06T06:53:02Z
department:
- _id: '101'
doi: 10.1093/imanum/12.3.429
intvolume: '        12'
issue: '3'
language:
- iso: eng
page: 429-455
publication: IMA Journal of Numerical Analysis
publication_status: published
status: public
title: Computational bifurcation of periodic solutions in systems with symmetry
type: journal_article
user_id: '32643'
volume: 12
year: '1992'
...
---
_id: '51585'
author:
- first_name: Joachim
  full_name: Hilgert, Joachim
  id: '220'
  last_name: Hilgert
citation:
  ama: Hilgert J. Fomenko, A.T. Symplectic Geometry (Gordon and Breach, 1988). <i>JBer
    DMV</i>. 1992;94.
  apa: Hilgert, J. (1992). Fomenko, A.T. Symplectic Geometry (Gordon and Breach, 1988).
    In <i>JBer. DMV</i> (Vol. 94).
  bibtex: '@article{Hilgert_1992, title={Fomenko, A.T. Symplectic Geometry (Gordon
    and Breach, 1988)}, volume={94}, journal={JBer. DMV}, author={Hilgert, Joachim},
    year={1992} }'
  chicago: Hilgert, Joachim. “Fomenko, A.T. Symplectic Geometry (Gordon and Breach,
    1988).” <i>JBer. DMV</i>, 1992.
  ieee: J. Hilgert, “Fomenko, A.T. Symplectic Geometry (Gordon and Breach, 1988),”
    <i>JBer. DMV</i>, vol. 94. 1992.
  mla: Hilgert, Joachim. “Fomenko, A.T. Symplectic Geometry (Gordon and Breach, 1988).”
    <i>JBer. DMV</i>, vol. 94, 1992.
  short: J. Hilgert, JBer. DMV 94 (1992).
date_created: 2024-02-20T12:24:52Z
date_updated: 2024-02-20T13:35:07Z
department:
- _id: '91'
extern: '1'
intvolume: '        94'
language:
- iso: eng
publication: JBer. DMV
publication_status: published
status: public
title: Fomenko, A.T. Symplectic Geometry (Gordon and Breach, 1988)
type: review
user_id: '49063'
volume: 94
year: '1992'
...
---
_id: '51442'
author:
- first_name: Joachim
  full_name: Hilgert, Joachim
  id: '220'
  last_name: Hilgert
- first_name: G.
  full_name: Ólafsson, G.
  last_name: Ólafsson
citation:
  ama: Hilgert J, Ólafsson G. Analytic Extensions of Representations, the Solvable
    Case. <i>Japan J Math</i>. 1992;18:213-290.
  apa: Hilgert, J., &#38; Ólafsson, G. (1992). Analytic Extensions of Representations,
    the Solvable Case. <i>Japan. J. Math.</i>, <i>18</i>, 213–290.
  bibtex: '@article{Hilgert_Ólafsson_1992, title={Analytic Extensions of Representations,
    the Solvable Case}, volume={18}, journal={Japan. J. Math.}, author={Hilgert, Joachim
    and Ólafsson, G.}, year={1992}, pages={213–290} }'
  chicago: 'Hilgert, Joachim, and G. Ólafsson. “Analytic Extensions of Representations,
    the Solvable Case.” <i>Japan. J. Math.</i> 18 (1992): 213–90.'
  ieee: J. Hilgert and G. Ólafsson, “Analytic Extensions of Representations, the Solvable
    Case,” <i>Japan. J. Math.</i>, vol. 18, pp. 213–290, 1992.
  mla: Hilgert, Joachim, and G. Ólafsson. “Analytic Extensions of Representations,
    the Solvable Case.” <i>Japan. J. Math.</i>, vol. 18, 1992, pp. 213–90.
  short: J. Hilgert, G. Ólafsson, Japan. J. Math. 18 (1992) 213–290.
date_created: 2024-02-19T07:33:18Z
date_updated: 2024-02-20T13:35:12Z
department:
- _id: '91'
extern: '1'
intvolume: '        18'
language:
- iso: eng
page: 213-290
publication: Japan. J. Math.
publication_status: published
status: public
title: Analytic Extensions of Representations, the Solvable Case
type: journal_article
user_id: '49063'
volume: 18
year: '1992'
...
---
_id: '51443'
author:
- first_name: Joachim
  full_name: Hilgert, Joachim
  id: '220'
  last_name: Hilgert
citation:
  ama: Hilgert J. Controllability on Real Reductive Groups. <i>Math Zeitschrift</i>.
    1992;209:463-466.
  apa: Hilgert, J. (1992). Controllability on Real Reductive Groups. <i>Math. Zeitschrift</i>,
    <i>209</i>, 463–466.
  bibtex: '@article{Hilgert_1992, title={Controllability on Real Reductive Groups},
    volume={209}, journal={Math. Zeitschrift}, author={Hilgert, Joachim}, year={1992},
    pages={463–466} }'
  chicago: 'Hilgert, Joachim. “Controllability on Real Reductive Groups.” <i>Math.
    Zeitschrift</i> 209 (1992): 463–66.'
  ieee: J. Hilgert, “Controllability on Real Reductive Groups,” <i>Math. Zeitschrift</i>,
    vol. 209, pp. 463–466, 1992.
  mla: Hilgert, Joachim. “Controllability on Real Reductive Groups.” <i>Math. Zeitschrift</i>,
    vol. 209, 1992, pp. 463–66.
  short: J. Hilgert, Math. Zeitschrift 209 (1992) 463–466.
date_created: 2024-02-19T07:34:43Z
date_updated: 2024-02-20T13:35:10Z
department:
- _id: '91'
extern: '1'
intvolume: '       209'
language:
- iso: eng
page: 463-466
publication: Math. Zeitschrift
publication_status: published
status: public
title: Controllability on Real Reductive Groups
type: journal_article
user_id: '49063'
volume: 209
year: '1992'
...
---
_id: '54832'
author:
- first_name: Margit
  full_name: Rösler, Margit
  id: '37390'
  last_name: Rösler
citation:
  ama: Rösler M. <i>Durch orthogonale trigonometrische Systeme auf dem Einheitskreis
    induzierte Faltunsstrukturen auf Z</i>.; 1992.
  apa: Rösler, M. (1992). <i>Durch orthogonale trigonometrische Systeme auf dem Einheitskreis
    induzierte Faltunsstrukturen auf Z</i>.
  bibtex: '@book{Rösler_1992, place={TU München}, title={Durch orthogonale trigonometrische
    Systeme auf dem Einheitskreis induzierte Faltunsstrukturen auf Z}, author={Rösler,
    Margit}, year={1992} }'
  chicago: Rösler, Margit. <i>Durch orthogonale trigonometrische Systeme auf dem Einheitskreis
    induzierte Faltunsstrukturen auf Z</i>. TU München, 1992.
  ieee: M. Rösler, <i>Durch orthogonale trigonometrische Systeme auf dem Einheitskreis
    induzierte Faltunsstrukturen auf Z</i>. TU München, 1992.
  mla: Rösler, Margit. <i>Durch orthogonale trigonometrische Systeme auf dem Einheitskreis
    induzierte Faltunsstrukturen auf Z</i>. 1992.
  short: M. Rösler, Durch orthogonale trigonometrische Systeme auf dem Einheitskreis
    induzierte Faltunsstrukturen auf Z, TU München, 1992.
date_created: 2024-06-20T06:57:59Z
date_updated: 2024-08-13T09:43:04Z
department:
- _id: '555'
language:
- iso: ger
place: TU München
status: public
title: Durch orthogonale trigonometrische Systeme auf dem Einheitskreis induzierte
  Faltunsstrukturen auf Z
type: dissertation
user_id: '82981'
year: '1992'
...
---
_id: '51588'
author:
- first_name: Joachim
  full_name: Hilgert, Joachim
  id: '220'
  last_name: Hilgert
citation:
  ama: Hilgert J. Varadarajan, V.S. An Introduction to Harmonic Analysis on Semisimple
    Lie Groups (Cambridge University Press, 1989). <i>JBer DMV</i>. 1991;94(4).
  apa: Hilgert, J. (1991). Varadarajan, V.S. An Introduction to Harmonic Analysis
    on Semisimple Lie Groups (Cambridge University Press, 1989). In <i>JBer. DMV</i>
    (Vol. 94, Issue 4).
  bibtex: '@article{Hilgert_1991, title={Varadarajan, V.S. An Introduction to Harmonic
    Analysis on Semisimple Lie Groups (Cambridge University Press, 1989)}, volume={94},
    number={4}, journal={JBer. DMV}, author={Hilgert, Joachim}, year={1991} }'
  chicago: Hilgert, Joachim. “Varadarajan, V.S. An Introduction to Harmonic Analysis
    on Semisimple Lie Groups (Cambridge University Press, 1989).” <i>JBer. DMV</i>,
    1991.
  ieee: J. Hilgert, “Varadarajan, V.S. An Introduction to Harmonic Analysis on Semisimple
    Lie Groups (Cambridge University Press, 1989),” <i>JBer. DMV</i>, vol. 94, no.
    4. 1991.
  mla: Hilgert, Joachim. “Varadarajan, V.S. An Introduction to Harmonic Analysis on
    Semisimple Lie Groups (Cambridge University Press, 1989).” <i>JBer. DMV</i>, vol.
    94, no. 4, 1991.
  short: J. Hilgert, JBer. DMV 94 (1991).
date_created: 2024-02-20T12:25:59Z
date_updated: 2024-02-20T13:35:16Z
department:
- _id: '91'
extern: '1'
intvolume: '        94'
issue: '4'
language:
- iso: eng
publication: JBer. DMV
publication_status: published
status: public
title: Varadarajan, V.S. An Introduction to Harmonic Analysis on Semisimple Lie Groups
  (Cambridge University Press, 1989)
type: review
user_id: '49063'
volume: 94
year: '1991'
...
---
_id: '51589'
author:
- first_name: Joachim
  full_name: Hilgert, Joachim
  id: '220'
  last_name: Hilgert
citation:
  ama: Hilgert J. Terras, A. Harmonic Analysis on Symmetric Spaces I and II (Springer,
    New York, 1985 und 1988). <i>JBer DMV</i>. 1991;93(2).
  apa: Hilgert, J. (1991). Terras, A. Harmonic Analysis on Symmetric Spaces I and
    II (Springer, New York, 1985 und 1988). In <i>JBer. DMV</i> (Vol. 93, Issue 2).
  bibtex: '@article{Hilgert_1991, title={Terras, A. Harmonic Analysis on Symmetric
    Spaces I and II (Springer, New York, 1985 und 1988)}, volume={93}, number={2},
    journal={JBer. DMV}, author={Hilgert, Joachim}, year={1991} }'
  chicago: Hilgert, Joachim. “Terras, A. Harmonic Analysis on Symmetric Spaces I and
    II (Springer, New York, 1985 Und 1988).” <i>JBer. DMV</i>, 1991.
  ieee: J. Hilgert, “Terras, A. Harmonic Analysis on Symmetric Spaces I and II (Springer,
    New York, 1985 und 1988),” <i>JBer. DMV</i>, vol. 93, no. 2. 1991.
  mla: Hilgert, Joachim. “Terras, A. Harmonic Analysis on Symmetric Spaces I and II
    (Springer, New York, 1985 Und 1988).” <i>JBer. DMV</i>, vol. 93, no. 2, 1991.
  short: J. Hilgert, JBer. DMV 93 (1991).
date_created: 2024-02-20T12:26:30Z
date_updated: 2024-02-20T13:35:18Z
department:
- _id: '91'
extern: '1'
intvolume: '        93'
issue: '2'
language:
- iso: eng
publication: JBer. DMV
publication_status: published
status: public
title: Terras, A. Harmonic Analysis on Symmetric Spaces I and II (Springer, New York,
  1985 und 1988)
type: review
user_id: '49063'
volume: 93
year: '1991'
...
---
_id: '51445'
author:
- first_name: Joachim
  full_name: Hilgert, Joachim
  id: '220'
  last_name: Hilgert
- first_name: G.
  full_name: Ólafsson, G.
  last_name: Ólafsson
- first_name: B.
  full_name: Orsted, B.
  last_name: Orsted
citation:
  ama: Hilgert J, Ólafsson G, Orsted B. Hardy Spaces on Affine Symmetric Spaces. <i>J
    reine und angew Math</i>. 1991;415:189-218.
  apa: Hilgert, J., Ólafsson, G., &#38; Orsted, B. (1991). Hardy Spaces on Affine
    Symmetric Spaces. <i>J. Reine Und Angew. Math.</i>, <i>415</i>, 189–218.
  bibtex: '@article{Hilgert_Ólafsson_Orsted_1991, title={Hardy Spaces on Affine Symmetric
    Spaces}, volume={415}, journal={J. reine und angew. Math.}, author={Hilgert, Joachim
    and Ólafsson, G. and Orsted, B.}, year={1991}, pages={189–218} }'
  chicago: 'Hilgert, Joachim, G. Ólafsson, and B. Orsted. “Hardy Spaces on Affine
    Symmetric Spaces.” <i>J. Reine Und Angew. Math.</i> 415 (1991): 189–218.'
  ieee: J. Hilgert, G. Ólafsson, and B. Orsted, “Hardy Spaces on Affine Symmetric
    Spaces,” <i>J. reine und angew. Math.</i>, vol. 415, pp. 189–218, 1991.
  mla: Hilgert, Joachim, et al. “Hardy Spaces on Affine Symmetric Spaces.” <i>J. Reine
    Und Angew. Math.</i>, vol. 415, 1991, pp. 189–218.
  short: J. Hilgert, G. Ólafsson, B. Orsted, J. Reine Und Angew. Math. 415 (1991)
    189–218.
date_created: 2024-02-19T07:45:41Z
date_updated: 2024-02-20T13:35:25Z
department:
- _id: '91'
extern: '1'
intvolume: '       415'
language:
- iso: eng
page: 189-218
publication: J. reine und angew. Math.
publication_status: published
status: public
title: Hardy Spaces on Affine Symmetric Spaces
type: journal_article
user_id: '49063'
volume: 415
year: '1991'
...
---
_id: '51483'
author:
- first_name: Joachim
  full_name: Hilgert, Joachim
  id: '220'
  last_name: Hilgert
citation:
  ama: 'Hilgert J. Group Theoretical Aspects of Gödels Model. In: Hilgert J, ed. <i>Jahrbuch
    Der Gödel Gesellschaft</i>. ; 1991.'
  apa: Hilgert, J. (1991). Group Theoretical Aspects of Gödels Model. In J. Hilgert
    (Ed.), <i>Jahrbuch der Gödel Gesellschaft</i>.
  bibtex: '@inbook{Hilgert_1991, place={Wien}, title={Group Theoretical Aspects of
    Gödels Model}, booktitle={Jahrbuch der Gödel Gesellschaft}, author={Hilgert, Joachim},
    editor={Hilgert, Joachim}, year={1991} }'
  chicago: Hilgert, Joachim. “Group Theoretical Aspects of Gödels Model.” In <i>Jahrbuch
    Der Gödel Gesellschaft</i>, edited by Joachim Hilgert. Wien, 1991.
  ieee: J. Hilgert, “Group Theoretical Aspects of Gödels Model,” in <i>Jahrbuch der
    Gödel Gesellschaft</i>, J. Hilgert, Ed. Wien, 1991.
  mla: Hilgert, Joachim. “Group Theoretical Aspects of Gödels Model.” <i>Jahrbuch
    Der Gödel Gesellschaft</i>, edited by Joachim Hilgert, 1991.
  short: 'J. Hilgert, in: J. Hilgert (Ed.), Jahrbuch Der Gödel Gesellschaft, Wien,
    1991.'
date_created: 2024-02-19T10:10:02Z
date_updated: 2024-02-20T13:35:23Z
department:
- _id: '91'
editor:
- first_name: Joachim
  full_name: Hilgert, Joachim
  last_name: Hilgert
extern: '1'
language:
- iso: eng
place: Wien
publication: Jahrbuch der Gödel Gesellschaft
publication_status: published
status: public
title: Group Theoretical Aspects of Gödels Model
type: book_chapter
user_id: '49063'
year: '1991'
...
---
_id: '51444'
author:
- first_name: Joachim
  full_name: Hilgert, Joachim
  id: '220'
  last_name: Hilgert
citation:
  ama: Hilgert J. Infinitesimally Generated Subsemigroups of Motion Groups. <i>Rocky
    Mount J Math</i>. 1991;21:865-878.
  apa: Hilgert, J. (1991). Infinitesimally Generated Subsemigroups of Motion Groups.
    <i>Rocky Mount. J. Math.</i>, <i>21</i>, 865–878.
  bibtex: '@article{Hilgert_1991, title={Infinitesimally Generated Subsemigroups of
    Motion Groups}, volume={21}, journal={Rocky Mount. J. Math.}, author={Hilgert,
    Joachim}, year={1991}, pages={865–878} }'
  chicago: 'Hilgert, Joachim. “Infinitesimally Generated Subsemigroups of Motion Groups.”
    <i>Rocky Mount. J. Math.</i> 21 (1991): 865–78.'
  ieee: J. Hilgert, “Infinitesimally Generated Subsemigroups of Motion Groups,” <i>Rocky
    Mount. J. Math.</i>, vol. 21, pp. 865–878, 1991.
  mla: Hilgert, Joachim. “Infinitesimally Generated Subsemigroups of Motion Groups.”
    <i>Rocky Mount. J. Math.</i>, vol. 21, 1991, pp. 865–78.
  short: J. Hilgert, Rocky Mount. J. Math. 21 (1991) 865–878.
date_created: 2024-02-19T07:43:02Z
date_updated: 2024-02-20T13:35:28Z
department:
- _id: '91'
extern: '1'
intvolume: '        21'
language:
- iso: eng
page: 865-878
publication: Rocky Mount. J. Math.
publication_status: published
status: public
title: Infinitesimally Generated Subsemigroups of Motion Groups
type: journal_article
user_id: '49063'
volume: 21
year: '1991'
...
---
_id: '51586'
author:
- first_name: Joachim
  full_name: Hilgert, Joachim
  id: '220'
  last_name: Hilgert
citation:
  ama: Hilgert J. Onishchik, A.L., und E.B. Vinberg. Lie Groups and Algebraic Groups
    (Springer, New York, 1990). <i>Zentralblatt</i>. 1991;722.
  apa: Hilgert, J. (1991). Onishchik, A.L., und E.B. Vinberg. Lie Groups and Algebraic
    Groups (Springer, New York, 1990). In <i>Zentralblatt</i> (Vol. 722).
  bibtex: '@article{Hilgert_1991, title={Onishchik, A.L., und E.B. Vinberg. Lie Groups
    and Algebraic Groups (Springer, New York, 1990)}, volume={722}, journal={Zentralblatt},
    author={Hilgert, Joachim}, year={1991} }'
  chicago: Hilgert, Joachim. “Onishchik, A.L., Und E.B. Vinberg. Lie Groups and Algebraic
    Groups (Springer, New York, 1990).” <i>Zentralblatt</i>, 1991.
  ieee: J. Hilgert, “Onishchik, A.L., und E.B. Vinberg. Lie Groups and Algebraic Groups
    (Springer, New York, 1990),” <i>Zentralblatt</i>, vol. 722. 1991.
  mla: Hilgert, Joachim. “Onishchik, A.L., Und E.B. Vinberg. Lie Groups and Algebraic
    Groups (Springer, New York, 1990).” <i>Zentralblatt</i>, vol. 722, 1991.
  short: J. Hilgert, Zentralblatt 722 (1991).
date_created: 2024-02-20T12:25:25Z
date_updated: 2024-02-20T13:35:54Z
department:
- _id: '91'
extern: '1'
intvolume: '       722'
language:
- iso: eng
publication: Zentralblatt
publication_status: published
status: public
title: Onishchik, A.L., und E.B. Vinberg. Lie Groups and Algebraic Groups (Springer,
  New York, 1990)
type: review
user_id: '49063'
volume: 722
year: '1991'
...
