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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

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Bibliographic databases:

UDC: 517.28, 517.54, 517.41
MSC: 14R15
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
\Bibitem{Sta17} \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} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000409223900007} \elib{http://elibrary.ru/item.asp?id=29450650}