Geodesic
Some transversality theorems
Sbornik. Mathematics, Tome 14 (1971) no. 1, pp. 140-156

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In this paper transversality theorems are proved for canonical transformations, contact transformations, and transformations which preserve volume elements, as well as sections of a fiber bundle whose base and fiber are smooth manifolds. Let $\Omega$ be one of the mapping spaces mentioned, and let $L$ be a smooth submanifold in the space of $r$-jets of the germs of the mappings in $\Omega$. The transversality theorem asserts that a set of mappings in $\Omega$ whose $r$-jet extensions are transversal to $L$ is everywhere dense in $\Omega$. Bibliography: 7 titles. 
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     title = {Some transversality theorems},
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S. M. Vishik. Some transversality theorems. Sbornik. Mathematics, Tome 14 (1971) no. 1, pp. 140-156. http://geodesic.mathdoc.fr/item/SM_1971_14_1_a8/