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Mat. Sb., 2007, Volume 198, Number 4, Pages 47–78 (Mi msb1542)  

This article is cited in 3 scientific papers (total in 3 papers)

Contact degeneracies of closed 2-forms

D. B. Zot'ev

Volgograd State Technical University

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.

DOI: https://doi.org/10.4213/sm1542

Full text: PDF file (694 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2007, 198:4, 491–520

Bibliographic databases:

UDC: 514.745.4+514.154+514.763.337+514.763.34
MSC: Primary 53D05, 53D10, 58F05; Secondary 53D20, 53D22
Received: 27.02.2006 and 18.08.2006

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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  • https://doi.org/10.4213/sm1542
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Zotev D.B., “Kontaktnye vyrozhdeniya tenzora elektromagnitnogo polya”, Vestn. Mosk. energeticheskogo in-ta, 2011, no. 2, 134–135  elib
    2. D. B. Zot'ev, “Fomenko–Zieschang invariants of integrable systems with symplectic singularities”, Russian Math. (Iz. VUZ), 56:1 (2012), 19–26  mathnet  crossref  mathscinet
    3. D. B. Zotev, “Predkvantovanie po Kostantu simplekticheskikh mnogoobrazii s kontaktnymi osobennostyami”, Matem. zametki, 105:6 (2019), 857–878  mathnet  crossref
  • Математический сборник Sbornik: Mathematics (from 1967)
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