The level set of a~smooth mapping in a~neighborhood of a~singular point, and zeros of a~quadratic mapping
Sbornik. Mathematics, Tome 73 (1992) no. 2, pp. 455-466
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The level set $M$ of a smooth mapping $F$ in a neighborhood of an anormal point is investigated. Concepts of 2-regularity are introduced for it. It is proved that if the mapping is 2-regular at the point under consideration, then in a neighborhood of it the set $M$ is locally diffeomorphic to the set of zeros of the second differential of $F$.
@article{SM_1992_73_2_a8,
author = {E. R. Avakov and A. A. Agrachev and A. V. Arutyunov},
title = {The level set of a~smooth mapping in a~neighborhood of a~singular point, and zeros of a~quadratic mapping},
journal = {Sbornik. Mathematics},
pages = {455--466},
publisher = {mathdoc},
volume = {73},
number = {2},
year = {1992},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_1992_73_2_a8/}
}
TY - JOUR AU - E. R. Avakov AU - A. A. Agrachev AU - A. V. Arutyunov TI - The level set of a~smooth mapping in a~neighborhood of a~singular point, and zeros of a~quadratic mapping JO - Sbornik. Mathematics PY - 1992 SP - 455 EP - 466 VL - 73 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/SM_1992_73_2_a8/ LA - en ID - SM_1992_73_2_a8 ER -
%0 Journal Article %A E. R. Avakov %A A. A. Agrachev %A A. V. Arutyunov %T The level set of a~smooth mapping in a~neighborhood of a~singular point, and zeros of a~quadratic mapping %J Sbornik. Mathematics %D 1992 %P 455-466 %V 73 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/SM_1992_73_2_a8/ %G en %F SM_1992_73_2_a8
E. R. Avakov; A. A. Agrachev; A. V. Arutyunov. The level set of a~smooth mapping in a~neighborhood of a~singular point, and zeros of a~quadratic mapping. Sbornik. Mathematics, Tome 73 (1992) no. 2, pp. 455-466. http://geodesic.mathdoc.fr/item/SM_1992_73_2_a8/