Geodesic
Jacobian conjecture, two-dimensional case
Problemy analiza, Tome 5 (2016) no. 2, pp. 69-78.

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

The Jacobian Conjecture was first formulated by O. Keller in 1939. In the modern form it supposes injectivity of the polynomial mapping $f$: $\mathbb{R}^n \to \mathbb{R}^n$ ($\mathbb{C}^n \to \mathbb{C}^n$) provided that jacobian $J_f\equiv \mathrm{const}\ne0$. In this note we consider structure of polynomial mappings $f$ that provide $J_f\equiv \mathrm{const} \ne0$.
Mots-clés : Jacobian conjecture. 
@article{PA_2016_5_2_a5,
     author = {V. V. Starkov},
     title = {Jacobian conjecture, two-dimensional case},
     journal = {Problemy analiza},
     pages = {69--78},
     publisher = {mathdoc},
     volume = {5},
     number = {2},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PA_2016_5_2_a5/}
}
TY  - JOUR
AU  - V. V. Starkov
TI  - Jacobian conjecture, two-dimensional case
JO  - Problemy analiza
PY  - 2016
SP  - 69
EP  - 78
VL  - 5
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PA_2016_5_2_a5/
LA  - en
ID  - PA_2016_5_2_a5
ER  - 
%0 Journal Article
%A V. V. Starkov
%T Jacobian conjecture, two-dimensional case
%J Problemy analiza
%D 2016
%P 69-78
%V 5
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PA_2016_5_2_a5/
%G en
%F PA_2016_5_2_a5
V. V. Starkov. Jacobian conjecture, two-dimensional case. Problemy analiza, Tome 5 (2016) no. 2, pp. 69-78. http://geodesic.mathdoc.fr/item/PA_2016_5_2_a5/

[1] Keller O.-H., “Ganze Cremona-Transformationen”, Monatshefte Math. Phys., 47 (1939), 299–306 | DOI | MR

[2] van den Essen A., Polynomial Automorphisms and the Jacobian Conjecture, Progress in Mathematics, 190, Birkhäuser Verlag, Basel, 2000 | MR | Zbl

[3] Drużkowski L. M., “On the global asymptotic stability problem and the Jacobian conjecture”, Control and Cybernetics, 34:3 (2005), 747–762 | MR | Zbl

[4] Pinchuk S., “A counterexample to the strong real Jacobian conjecture”, Math. Z., 217 (1994), 1–4 | DOI | MR | Zbl

[5] Yagzhev A. V., “Keller's problem”, Siberian Math. J., 21:5 (1980), 747–754 | DOI | MR | Zbl

[6] Kulikov V. S., “Generalized and local Jacobian problems”, Russian Academy of Sciences. Izvestiya Mathematics, 41:2 (1993), 351–365 | DOI | MR

[7] Wang S. S.-S., “A Jacobian criterion for separability”, J. of Algebra, 65:2 (1980), 453–494 | DOI | MR | Zbl

[8] Moh T. T., “On the global Jacobian conjecture and the configuration of roots”, J. reine und angew. Math., 340 (1983), 140–212 | MR | Zbl

[9] Smale S., “Mathematical Problems for the Next Century”, Math. Intelligencer, 20:2 (1998), 7–15 | DOI | MR | Zbl