The Jacobian conjecture: structure of Keller mappings
Problemy analiza, Tome 8 (2019) no. 3, pp. 152-165.

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

The Jacobian conjecture was first formulated by O. N. Keller in 1939. In the modern form it supposes injectivity of the polynomial mapping $f: \Bbb R^n \to \Bbb R^n$ ($\Bbb C^n \to \Bbb C^n$) under the assumption that $J_f\equiv const\ne0$. In this paper, we consider the structure of polynomial mappings $f$ with $J_f\equiv const \ne0$.
Keywords: Keller mapping.
Mots-clés : Jacobian conjecture
@article{PA_2019_8_3_a14,
     author = {V. V. Starkov},
     title = {The {Jacobian} conjecture: structure of {Keller} mappings},
     journal = {Problemy analiza},
     pages = {152--165},
     publisher = {mathdoc},
     volume = {8},
     number = {3},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PA_2019_8_3_a14/}
}
TY  - JOUR
AU  - V. V. Starkov
TI  - The Jacobian conjecture: structure of Keller mappings
JO  - Problemy analiza
PY  - 2019
SP  - 152
EP  - 165
VL  - 8
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PA_2019_8_3_a14/
LA  - en
ID  - PA_2019_8_3_a14
ER  - 
%0 Journal Article
%A V. V. Starkov
%T The Jacobian conjecture: structure of Keller mappings
%J Problemy analiza
%D 2019
%P 152-165
%V 8
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PA_2019_8_3_a14/
%G en
%F PA_2019_8_3_a14
V. V. Starkov. The Jacobian conjecture: structure of Keller mappings. Problemy analiza, Tome 8 (2019) no. 3, pp. 152-165. http://geodesic.mathdoc.fr/item/PA_2019_8_3_a14/

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

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

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

[4] Russian Academy of Sciences. Izvestiya Mathematics, 41:2 (1993), 351–365 | DOI | MR | Zbl

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

[6] Ponnusamy S., Starkov V. V., “The Jacobian Conjecture and Injectivity Conditions”, Bulletin of the Malaysian Mathematical Sciences Society, 41:4 (2018), 2099–2115 | DOI | MR | Zbl

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

[8] Starkov V. V., “Jacobian conjecture, two-dimensional case”, Probl. Anal. Issues Anal., 5(23):2 (2016), 69–78 | DOI | MR | Zbl

[9] Starkov V. V., “Structure of Keller mappings, two-dimensional case”, Probl. Anal. Issues Anal., 6(24):1 (2017), 68–81 | DOI | MR | Zbl

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