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Sbornik: Mathematics, 2007, Volume 198, Issue 4, Pages 491–520
DOI: https://doi.org/10.1070/SM2007v198n04ABEH003846 (Mi sm1542) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Contact degeneracies of closed 2-forms

D. B. Zot'ev

Volgograd State Technical University
English version PDF (405 kB) Citations (5)
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DOI: https://doi.org/10.1070/SM2007v198n04ABEH003846
Abstract: Consider a closed 2-form that is degenerate at the points of a hypersurface and is non-degenerate outside it. In the neighbourhood of a singularity (which is called contact under certain natural conditions) the limit behaviour of Hamiltonian fields is investigated and a canonical form of the 2-form is found (Darboux's theorem). Connections with regular Lie structures are established. Properties of integrable structures on Liouville tori containing contact degeneracies are studied.
Bibliography: 16 titles.
Received: 27.02.2006 and 18.08.2006
Russian version:
Matematicheskii Sbornik, 2007, Volume 198, Number 4, Pages 47–78
DOI: https://doi.org/10.4213/sm1542
Bibliographic databases:
UDC: 514.745.4+514.154+514.763.337+514.763.34
MSC: Primary 53D05, 53D10, 58F05; Secondary 53D20, 53D22
Language: English
Original paper language: Russian
Citation: D. B. Zot'ev, “Contact degeneracies of closed 2-forms”, Mat. Sb., 198:4 (2007), 47–78; Sb. Math., 198:4 (2007), 491–520
Citation in format AMSBIB
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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    Russian version PDF:256
    English version PDF:13
    References:74
    First page:4
     
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