Document Zbl 0465.58013

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Am. Math. Soc., New Ser.</a> <a href="/?q=in%3A146122" title="Articles in this Issue">5, 1-13 (1981)</a>. </div> <div class="abstract"><div class="scan"> <span> Page: <a class="goto" href="/scans/465/295.gif">−5</a> <a class="goto" href="/scans/465/296.gif">−4</a> <a class="goto" href="/scans/465/297.gif">−3</a> <a class="goto" href="/scans/465/298.gif">−2</a> <a class="goto" href="/scans/465/299.gif">−1</a> <a class="goto" href="/scans/465/300.gif">±0</a> <a class="goto" href="/scans/465/301.gif">+1</a> <a class="goto" href="/scans/465/302.gif">+2</a> <a class="goto" href="/scans/465/303.gif">+3</a> <a class="goto" href="/scans/465/304.gif">+4</a> <a class="goto" href="/scans/465/305.gif">+5</a></span> <a class="scan" href="/scans/465/300.gif">Show Scanned Page</a><br> <img src="/scans/465/300.gif" alt="scan of Zbl 0465.58013" onclick="$(this).siblings('.scan').click();"> </div> <div class="clearfix"></div></div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=ci%3A3729131">Cited in <strong>3</strong> Reviews</a></div><div class="clear"><a href="/?q=rf%3A3729131">Cited in <strong>55</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A53D50" title="MSC2020">53D50</a> </td> <td class="space"> Geometric quantization </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A53C15" title="MSC2020">53C15</a> </td> <td class="space"> General geometric structures on manifolds (almost complex, almost product structures, etc.) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A81Q99" title="MSC2020">81Q99</a> </td> <td class="space"> General mathematical topics and methods in quantum theory </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A37J99" title="MSC2020">37J99</a> </td> <td class="space"> Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A70Hxx" title="MSC2020">70Hxx</a> </td> <td class="space"> Hamiltonian and Lagrangian mechanics </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Asymplectic+geometry">symplectic geometry</a>; <a href="/?q=ut%3ALagrangian">Lagrangian</a>; <a href="/?q=ut%3ALagrange+bracket">Lagrange bracket</a>; <a href="/?q=ut%3AFourier+transform">Fourier transform</a>; <a href="/?q=ut%3Ageometric+quantization">geometric quantization</a>; <a href="/?q=ut%3Apolarization">polarization</a>; <a href="/?q=ut%3Asymplectomorphism">symplectomorphism</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 0465.58013" data-ciurl="/ci/03729131" data-biburl="/bibtex/03729131.bib" data-amsurl="/amsrefs/03729131.bib" data-xmlurl="/xml/03729131.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/03729131.pdf" title="Zbl 0465.58013 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1090/S0273-0979-1981-14911-9" aria-label="DOI for “Symplectic geometry”" title="10.1090/S0273-0979-1981-14911-9">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Ralph Abraham and Jerrold E. Marsden, Foundations of mechanics, Benjamin/Cummings Publishing Co., Inc., Advanced Book Program, Reading, Mass., 1978. Second edition, revised and enlarged; With the assistance of Tudor Raţiu and Richard Cushman. · <a href="/0393.70001" class="nowrap">Zbl 0393.70001</a></td> </tr><tr> <td>[2]</td> <td class="space">V. Arnold, Les méthodes mathématiques de la mécanique classique, Éditions Mir, Moscow, 1976 (French). Traduit du russe par Djilali Embarek. V. I. Arnol$^{\prime}$d, Mathematical methods of classical mechanics, Springer-Verlag, New York-Heidelberg, 1978. Translated from the Russian by K. Vogtmann and A. Weinstein; Graduate Texts in Mathematics, 60.</td> </tr><tr> <td>[3]</td> <td class="space">L. Auslander and B. Kostant, Polarization and unitary representations of solvable Lie groups, Invent. 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Sternberg, Hamiltonian group actions and dynamical systems of Calogero type, Comm. Pure Appl. Math. 31 (1978), no. 4, 481 – 507. · <a href="/0368.58008" class="nowrap">Zbl 0368.58008</a> · <a href="https://doi.org/10.1002/cpa.3160310405" class="nowrap">doi:10.1002/cpa.3160310405</a></td> </tr><tr> <td>[18]</td> <td class="space">A. A. Kirillov, Unitary representations of nilpotent Lie groups, Uspehi Mat. Nauk 17 (1962), no. 4 (106), 57 – 110 (Russian). · <a href="/0090.09802" class="nowrap">Zbl 0090.09802</a></td> </tr><tr> <td>[19]</td> <td class="space">A. A. Kirillov, Elements of the theory of representations, Springer-Verlag, Berlin-New York, 1976. Translated from the Russian by Edwin Hewitt; Grundlehren der Mathematischen Wissenschaften, Band 220. · <a href="/0342.22001" class="nowrap">Zbl 0342.22001</a></td> </tr><tr> <td>[20]</td> <td class="space">Bertram Kostant, Quantization and unitary representations. I. Prequantization, Lectures in modern analysis and applications, III, Springer, Berlin, 1970, pp. 87 – 208. Lecture Notes in Math., Vol. 170. · <a href="/0223.53028" class="nowrap">Zbl 0223.53028</a></td> </tr><tr> <td>[21]</td> <td class="space">Bertram Kostant, The solution to a generalized Toda lattice and representation theory, Adv. in Math. 34 (1979), no. 3, 195 – 338. · <a href="/0433.22008" class="nowrap">Zbl 0433.22008</a> · <a href="https://doi.org/10.1016/0001-8708(79)90057-4" class="nowrap">doi:10.1016/0001-8708(79)90057-4</a></td> </tr><tr> <td>[22]</td> <td class="space">J. L. Lagrange, Mémoire sur la théorie des variations des éléments des planètes, Mémoires de la classe des sciences mathématiques et physiques de l’institut de France, 1808, pp. 1-72.</td> </tr><tr> <td>[23]</td> <td class="space">J. L. Lagrange, Second mémoire sur la théorie de la variation des constantes arbitraires dans les problèmes de mécanique, Mémoires de la classe des sciences mathématiques et physiques de l’institut de France 1809, pp. 343-352.</td> </tr><tr> <td>[24]</td> <td class="space">Robert G. Littlejohn, A guiding center Hamiltonian: a new approach, J. Math. Phys. 20 (1979), no. 12, 2445 – 2458. · <a href="/0444.70020" class="nowrap">Zbl 0444.70020</a> · <a href="https://doi.org/10.1063/1.524053" class="nowrap">doi:10.1063/1.524053</a></td> </tr><tr> <td>[25]</td> <td class="space">G.-M. Marle, Symplectic manifolds, dynamical groups, and Hamiltonian mechanics, Differential geometry and relativity, Reidel, Dordrecht, 1976, pp. 249 – 269. Mathematical Phys. and Appl. Math., Vol. 3. · <a href="/0369.53042" class="nowrap">Zbl 0369.53042</a></td> </tr><tr> <td>[26]</td> <td class="space">Jerrold Marsden and Alan Weinstein, Reduction of symplectic manifolds with symmetry, Rep. 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