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A Geometric Solution to the Jacobian Problem

Yıl 2018, Sayı: 24, 44 - 49, 14.08.2018

Öz

In this article given a geometric solution to the well-known Jacobian problem. The twodimensional
polynomial Keller map is considered in four-dimensional Euclidean space R
4
. Used the concept
of parallel. A well-known example of Vitushkin is also considered. Earlier it was known that Vitushkin’s map
has a nonzero constant Jacobian and it is not injective. We will show that the Vitushkin map is not surjective
and moreover it has two inverse maps in the domain of its definition

Kaynakça

  • [1]Newman D. T., One-one polynomial maps, Proc. Amer. Math. Soc., 11, 1960, 867–870.
  • [2]Bialynicki-Birula A., Rosenlicht V., Injective morphisms of real algebraic varieties, Proc.of the AMS., 13, 1962 , 200–203.
  • [3]Yagzhev A. V., On Keller’s problem, Siberian Math.J., 21, 1980, 747–754.
  • [4]Bass H., Connel E., Wright D., The Jacobian Conjecture: Reduction of Degree and Formal Expansion of the Inverse, Bulletin of the AMS, №7 (1982), 287–330.
  • [5]S. Cynk and K. Rusek, Injective endomorphisms of algebraic and analytic sets, Annales Polonici Mathematici, 56 № 1 (1991), 29–35 .
  • [6]Aro van den Essen, Polynomial Automorphisms and the Jacobian Conjecture, Progress in Mathematics, 2000, 77–79 .
Yıl 2018, Sayı: 24, 44 - 49, 14.08.2018

Öz

Kaynakça

  • [1]Newman D. T., One-one polynomial maps, Proc. Amer. Math. Soc., 11, 1960, 867–870.
  • [2]Bialynicki-Birula A., Rosenlicht V., Injective morphisms of real algebraic varieties, Proc.of the AMS., 13, 1962 , 200–203.
  • [3]Yagzhev A. V., On Keller’s problem, Siberian Math.J., 21, 1980, 747–754.
  • [4]Bass H., Connel E., Wright D., The Jacobian Conjecture: Reduction of Degree and Formal Expansion of the Inverse, Bulletin of the AMS, №7 (1982), 287–330.
  • [5]S. Cynk and K. Rusek, Injective endomorphisms of algebraic and analytic sets, Annales Polonici Mathematici, 56 № 1 (1991), 29–35 .
  • [6]Aro van den Essen, Polynomial Automorphisms and the Jacobian Conjecture, Progress in Mathematics, 2000, 77–79 .
Toplam 6 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Araştırma Makalesi
Yazarlar

Kerimbayev Rashid Konyrbayevich Bu kişi benim

Yayımlanma Tarihi 14 Ağustos 2018
Gönderilme Tarihi 19 Şubat 2018
Yayımlandığı Sayı Yıl 2018 Sayı: 24

Kaynak Göster

APA Konyrbayevich, K. R. (2018). A Geometric Solution to the Jacobian Problem. Journal of New Theory(24), 44-49.
AMA Konyrbayevich KR. A Geometric Solution to the Jacobian Problem. JNT. Ağustos 2018;(24):44-49.
Chicago Konyrbayevich, Kerimbayev Rashid. “A Geometric Solution to the Jacobian Problem”. Journal of New Theory, sy. 24 (Ağustos 2018): 44-49.
EndNote Konyrbayevich KR (01 Ağustos 2018) A Geometric Solution to the Jacobian Problem. Journal of New Theory 24 44–49.
IEEE K. R. Konyrbayevich, “A Geometric Solution to the Jacobian Problem”, JNT, sy. 24, ss. 44–49, Ağustos 2018.
ISNAD Konyrbayevich, Kerimbayev Rashid. “A Geometric Solution to the Jacobian Problem”. Journal of New Theory 24 (Ağustos 2018), 44-49.
JAMA Konyrbayevich KR. A Geometric Solution to the Jacobian Problem. JNT. 2018;:44–49.
MLA Konyrbayevich, Kerimbayev Rashid. “A Geometric Solution to the Jacobian Problem”. Journal of New Theory, sy. 24, 2018, ss. 44-49.
Vancouver Konyrbayevich KR. A Geometric Solution to the Jacobian Problem. JNT. 2018(24):44-9.


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