Geodesic
Stable lower estimates for smooth mappings and for gradients of smooth function
Sbornik. Mathematics, Tome 19 (1973) no. 3, pp. 425-467 
N. N. Nekhoroshev. Stable lower estimates for smooth mappings and for gradients of smooth function. Sbornik. Mathematics, Tome 19 (1973) no. 3, pp. 425-467. http://geodesic.mathdoc.fr/item/SM_1973_19_3_a4/
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     author = {N. N. Nekhoroshev},
     title = {Stable lower estimates for smooth mappings and for gradients of smooth function},
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     volume = {19},
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     url = {http://geodesic.mathdoc.fr/item/SM_1973_19_3_a4/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this article is discussed a stable lower estimate for gradients of functions near a critical point. It is stable in the sense that if the function belongs to a family of functions depending smoothly on a finite-dimensional parameter, then the estimate will be correct for functions with close parameter values. Related to this estimate is a stratification of the space of jets of functions; the strata are semialgebraic sets of increasing codimension. Bibliography: 6 titles.

[1] N. N. Nekhoroshev, “O povedenii gamiltonovykh sistem, blizkikh k integriruemym”, Funkts. analiz, 5:4 (1971), 82–83 | MR | Zbl

[2] V. M. Zakalyukin, “Algebraicheskaya vychislimost indeksa osoboi tochki vektornogo polya”, Funkts. analiz, 6:1 (1972), 77–78 | MR | Zbl

[3] I. R. Shafarevich, “Osnovy algebraicheskoi geometrii”, Uspekhi matem. nauk, XXIV:6 (150) (1969), 3–184 | MR

[4] E. A. Gorin, “Ob asimptoticheskikh svoistvakh mnogochlenov i algebraicheskikh funktsii ot neskolkikh peremennykh”, Uspekhi matem. nauk, XVI:1 (97) (1961), 91–118 | MR

[5] A. I. Markushevich, Kratkii kurs teorii analiticheskikh funktsii, izd-vo «Nauka», Moskva, 1966 | MR

[6] B. V. Shabat, Vvedenie v kompleksnyi analiz, izd-vo «Nauka», Moskva, 1969 | MR