Geodesic
Contact degeneracies of closed 2-forms
Sbornik. Mathematics, Tome 198 (2007) no. 4, pp. 491-520

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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. 
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     author = {D. B. Zot'ev},
     title = {Contact degeneracies of closed  2-forms},
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D. B. Zot'ev. Contact degeneracies of closed  2-forms. Sbornik. Mathematics, Tome 198 (2007) no. 4, pp. 491-520. http://geodesic.mathdoc.fr/item/SM_2007_198_4_a2/