Geodesic
Some transversality theorems
Sbornik. Mathematics, Tome 14 (1971) no. 1, pp. 140-156 
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/
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] V. I. Arnold, Lektsii po klassicheskoi mekhanike, t. II, MGU, Moskva, 1968

[2] Dzh. Mezer, “Strukturnaya ustoichivost otobrazhenii”, Osobennosti differentsiruemykh otobrazhenii, 1968, 216–267, Mir, Moskva | MR

[3] P. K. Rashevskii, Geometricheskaya teoriya uravnenii s chastnymi proizvodnymi, Gostekhizdat, Moskva–Leningrad, 1947

[4] R. Tom, G. Levin, “Osobennosti differentsiruemykh otobrazhenii”, Osobennosti differentsiruemykh otobrazhenii, 1968, 9–102, Mir, Moskva | MR

[5] L. P. Eizenkhart, Nepreryvnye gruppy preobrazovanii, IL, Moskva, 1947

[6] S. Lie, F. Engel, Theorie der Transformationsgruppen, s. 2, Teubner, Leipzig, 1888 (1930)

[7] R. Thom, “Ensembles et morphisms stratifies”, Bull. Amer. Math. Soc., 75:2 (1969), 240–284 | DOI | MR | Zbl