Geodesic
Smooth Functions, Formal Series, and Whitney
Matematičeskoe obrazovanie, Tome 79 (2016) no. 3, pp. 49-65.

Voir la notice de l'article provenant de la source Math-Net.Ru

An introduction to smooth calculus including a number of Whitney theorems.
Keywords: smooth functions, formal series, Whitney theorem. 
@article{MO_2016_79_3_a5,
     author = {N. G. Pavlova and A. O. Remizov},
     title = {Smooth {Functions,} {Formal} {Series,} and {Whitney}},
     journal = {Matemati\v{c}eskoe obrazovanie},
     pages = {49--65},
     publisher = {mathdoc},
     volume = {79},
     number = {3},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MO_2016_79_3_a5/}
}
TY  - JOUR
AU  - N. G. Pavlova
AU  - A. O. Remizov
TI  - Smooth Functions, Formal Series, and Whitney
JO  - Matematičeskoe obrazovanie
PY  - 2016
SP  - 49
EP  - 65
VL  - 79
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MO_2016_79_3_a5/
LA  - ru
ID  - MO_2016_79_3_a5
ER  - 
%0 Journal Article
%A N. G. Pavlova
%A A. O. Remizov
%T Smooth Functions, Formal Series, and Whitney
%J Matematičeskoe obrazovanie
%D 2016
%P 49-65
%V 79
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MO_2016_79_3_a5/
%G ru
%F MO_2016_79_3_a5
N. G. Pavlova; A. O. Remizov. Smooth Functions, Formal Series, and Whitney. Matematičeskoe obrazovanie, Tome 79 (2016) no. 3, pp. 49-65. http://geodesic.mathdoc.fr/item/MO_2016_79_3_a5/

[1] Arnold V.I., Dopolnitelnye glavy teorii obyknovennykh differentsialnykh uravnenii, Nauka, M., 1978, 304 pp. <ext-link ext-link-type='mr-item-id' href='http://mathscinet.ams.org/mathscinet-getitem?mr=526218'>526218</ext-link>

[2] Arnold V.I., Geometricheskie metody v teorii obyknovennykh differentsialnykh uravnenii, Izd-vo Udmurtskogo gos. un-ta, Izhevsk, 2000, 400 pp.

[3] Breker T., Lander L., Differentsiruemye rostki i katastrofy, Mir, M., 1977

[4] Golubitskii M., Giiemin V., Ustoichivye otobrazheniya i ikh osobennosti, Mir, M., 1977, 290 pp. <ext-link ext-link-type='mr-item-id' href='http://mathscinet.ams.org/mathscinet-getitem?mr=467801'>467801</ext-link>

[5] Dubrovin B.A., Novikov S.P., Fomenko A.T., Sovremennaya geometriya, Nauka, M., 1984 <ext-link ext-link-type='mr-item-id' href='http://mathscinet.ams.org/mathscinet-getitem?mr=766739'>766739</ext-link>

[6] Zorich V.A., Matematicheskii analiz, Nauka, M., 1981 <ext-link ext-link-type='mr-item-id' href='http://mathscinet.ams.org/mathscinet-getitem?mr=665257'>665257</ext-link>

[7] Narasimkhan R., Analiz na deistvitelnykh i kompleksnykh mnogoobraziyakh, Mir, M., 1971

[8] Whitney H., “On Singularities of Mappings of Euclidean Spaces. I. Mappings of the Plane into the Plane”, Annals of Mathematics, Second Series, 62:3 (1955), 374–410 <ext-link ext-link-type='doi' href='https://doi.org/10.2307/1970070'>10.2307/1970070</ext-link><ext-link ext-link-type='mr-item-id' href='http://mathscinet.ams.org/mathscinet-getitem?mr=73980'>73980</ext-link><ext-link ext-link-type='zbl-item-id' href='https://zbmath.org/?q=an:0068.37101'>0068.37101</ext-link>