Geodesic
Smooth functions, formal series, Whitney theorems, finished
Matematičeskoe obrazovanie, no. 3 (2017), pp. 13-27 Cet article a éte moissonné depuis la source Math-Net.Ru

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This is the final part of the paper published in the same journal one year ago. We continue to acquaint the reader with basic facts of singularity theory, for instance, division theorem, Malgrange preparation theorem, and we give the proof of Whitney theorem on mappings of the plane into the plane.
Keywords: the theory of singularities of smooth mappings, the division theorem, the Malgrange preparation theorem, Whitney's theorem on mappings of the plane into the plane. 
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     author = {N. G. Pavlova and A. O. Remizov},
     title = {Smooth functions, formal series, {Whitney} theorems, finished},
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     url = {http://geodesic.mathdoc.fr/item/MO_2017_3_a2/}
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N. G. Pavlova; A. O. Remizov. Smooth functions, formal series, Whitney theorems, finished. Matematičeskoe obrazovanie, no. 3 (2017), pp. 13-27. http://geodesic.mathdoc.fr/item/MO_2017_3_a2/

[1] Arnold V.I., Varchenko A.N., Gusein-Zade S.M., Osobennosti differentsiruemykh otobrazhenii, MTsNMO, M., 2004. | MR

[2] Arnold V.I., Teoriya katastrof, Nauka, M., 1990. | MR

[3] Arnold V.I., Gyuigens i Barrou, Nyuton i Guk, Nauka, M., 1989. | MR

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

[5] Vinberg E.B., Kurs algebry, Faktorial, M., 2002.

[6] Golubitskii M., Giiemin V., Ustoichivye otobrazheniya i ikh osobennosti, Mir, M., 1977. | MR

[7] Zorich V.A., Matematicheskii analiz, Nauka, M., 1981 | MR

[8] Malgranzh B., Idealy differentsiruemykh funktsii, Mir, M., 1968.

[9] Mischenko A.S., Fomenko A.T., Kurs differentsialnoi geometrii i topologii, Faktorial, M., 2000. | MR

[10] Pavlova N.G., Remizov A.O., “Gladkie funktsii, formalnye ryady i teoremy Uitni”, Matematicheskoe obrazovanie, 2016, no. 3(79), 49–65

[11] 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 | DOI | MR | Zbl