Geodesic
Symplectic Geometry of Manifolds with Almost Nowhere Vanishing Closed 2-Form
Matematičeskie zametki, Tome 76 (2004) no. 1, pp. 66-77

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We study local geometric properties of manifolds equipped with a closed 2-form nondegenerate at all points of a dense proper subset. We introduce the natural notion of tame singular point, at which the matrix of the 2-form degenerates in a regular way. We find a condition for Hamiltonian dynamical systems to be extended smoothly to tame singular points, generalize the Darboux theorem about the local reduction of the matrix of the 2-form to canonical form, and study the singular behavior of directional gradients. 
@article{MZM_2004_76_1_a6,
     author = {D. B. Zot'ev},
     title = {Symplectic {Geometry} of {Manifolds} with {Almost} {Nowhere} {Vanishing} {Closed} {2-Form}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {66--77},
     publisher = {mathdoc},
     volume = {76},
     number = {1},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2004_76_1_a6/}
}
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D. B. Zot'ev. Symplectic Geometry of Manifolds with Almost Nowhere Vanishing Closed 2-Form. Matematičeskie zametki, Tome 76 (2004) no. 1, pp. 66-77. http://geodesic.mathdoc.fr/item/MZM_2004_76_1_a6/