Geodesic
Some properties of two-dimensional surjective $p$-homogeneous maps
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 7, pp. 1083-1092 
A. V. Arutyunov; S. E. Zhukovskiy; D. Yu. Karamzin. Some properties of two-dimensional surjective $p$-homogeneous maps. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 7, pp. 1083-1092. http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_7_a0/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The properties of real $p$-homogeneous polynomial maps in $\mathrm{R}^2$ are examined. The relation between surjectivity and the existence of a nontrivial zero is investigated. Additionally, the relation between surjectivity and stable surjectivity is studied. Examples are discussed.

[1] Vasilev F. P., Metody optimizatsii, Faktorial press, M., 2002

[2] Polyak B. T., Vvedenie v optimizatsiyu, Nauka, M., 1983

[3] Golishnikov M. M., Izmailov A. F., “Nyutonovskie metody dlya zadach uslovnoi optimizatsii s neregulyarnymi ogranicheniyami”, Zh. vychisl. matem. i matem. fiz., 46:8 (2006), 1369–1391

[4] Kovalev M. D., “Kvadratichnye i rychazhnye otobrazheniya”, Tr. MIAN, 239, 2002, 195–214 | Zbl

[5] Kovalev M. D., “Nekotorye svoistva rychazhnykh otobrazhenii”, Fundament. i prikl. matem., 12:1 (2006), 129–142 | Zbl

[6] Agrachev A. A., “Topologiya kvadratichnykh otobrazhenii i gessiany gladkikh otobrazhenii”, Itogi nauki i tekhn. Ser. Algebra. Topol. Geom., 26, VINITI, M., 1988, 85–124

[7] Arutyunov A. V., “Neotritsatelnost kvadratichnykh form na peresechenii kvadrik i kvadratichnye otobrazheniya”, Matem. zametki, 84:2 (2008), 163–174 | DOI | Zbl

[8] Arutyunov A. V., Zhukovskii S. E., “Svoistva syur'ektivnykh veschestvennykh kvadratichnykh otobrazhenii”, Matem. sbornik, 207:9 (2016), 3–34 | DOI

[9] Arutyunov A. V., Zhukovskii S. E., “O syur'ektivnykh kvadratichnykh otobrazheniyakh”, Matem. zametki, 99:2 (2016), 181–185 | DOI | Zbl

[10] Bochnak J., Coste M., Roy M. F., Real algebraic geometry, A Series of Modern Surveys in Mathematics, Springer, Berlin, 1998 | MR | Zbl

[11] Fomenko A. T., Fuks D. B., Kurs gomotopicheskoi topologii, Nauka, M., 1989

[12] Avakov E. R., Arutyunov A. V., Karamzin D. Yu., “Issledovanie gladkikh otobrazhenii v okrestnosti anormalnoi tochki”, Izvestiya RAN. Ser. matem., 78:2 (2014), 3–44 | DOI

[13] Arutyunov A. V., Optimality conditions: Abnormal and degenerate problems, Math. Appl., Kluwer Acad. Publisher, Berlin, 2000 | MR | Zbl

[14] Arutyunov A. V., “Gladkie anormalnye zadachi teorii ekstremuma i analiza”, Uspekhi matem. nauk, 67:3(405) (2012), 3–62 | DOI

[15] Karamzin D. Yu., “Teorema Dainsa i nekotorye drugie svoistva kvadratichnykh otobrazhenii”, Zh. vychisl. matem. i matem. fiz., 55:10 (2015), 1661–1669 | DOI | Zbl