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Probl. Anal. Issues Anal., 2017, Volume 6(24), Issue 1, Pages 68–81 (Mi pa212)  

Structure of Keller mappings, two-dimensional case

V. V. Starkov

Petrozavodsk State University, 33, Lenina pr., Petrozavodsk 185910, Russia

Abstract: A Keller map is a polynomial mapping $f: \Bbb R^n \to \Bbb R^n$ (or $\Bbb C^n \to \Bbb C^n$) with the Jacobian $J_f\equiv \mathrm{const}\ne0$. The Jacobian conjecture was first formulated by O. N. Keller in 1939. In the modern form it supposes injectivity of a Keller map. Earlier, in the case $n=2$, the author gave a complete description of Keller maps with $\deg f\le 3.$ This paper is devoted to the description of Keller maps for which $\deg f\le 4.$ Significant differences between these two cases are revealed, which, in particular, indicate the irregular structure of Keller maps even in the case of $n=2$.

Keywords: Jacobian conjecture, Keller maps.

Funding Agency Grant Number
Russian Science Foundation 17-11-01229
The work is supported by the Russian Science Foundation under grant 17-11-01229 and performed in Petrozavodsk State University


DOI: https://doi.org/10.15393/j3.art.2017.3870

Full text: PDF file (371 kB)
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Bibliographic databases:

UDC: 517.28, 517.54, 517.41
MSC: 14R15
Received: 24.05.2017
Revised: 08.06.2017
Accepted:08.06.2017
Language:

Citation: V. V. Starkov, “Structure of Keller mappings, two-dimensional case”, Probl. Anal. Issues Anal., 6(24):1 (2017), 68–81

Citation in format AMSBIB
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\by V.~V.~Starkov
\paper Structure of Keller mappings, two-dimensional case
\jour Probl. Anal. Issues Anal.
\yr 2017
\vol 6(24)
\issue 1
\pages 68--81
\mathnet{http://mi.mathnet.ru/pa212}
\crossref{https://doi.org/10.15393/j3.art.2017.3870}
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\elib{http://elibrary.ru/item.asp?id=29450650}


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