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J. Sib. Fed. Univ. Math. Phys., 2018, Volume 11, Issue 6, Pages 776–780 (Mi jsfu726)  

Jacobian conjecture for mappings of a special type in ${\mathbb C}^2$

Maria A. Stepanova

Faculty of Mathematics and Mechanics, Lomonosov Moscow State University, Leninskie Gory, GSP-2, Moscow, 119992, Russia

Abstract: We show that a polynomial mapping of the type $ (x \rightarrow F[x+f(a(x)+b(y))],  y \rightarrow G[y+g(c(x)+d(y))])$, where $(a,b,c,d,f,g,F,G)$ are polynomials with non-zero Jacobian is a composition of no more than 3 linear or triangular transformations. This result, however, leaves the possibility of existence of a counterexample of polynomial complexity two.

Keywords: analytical complexity.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation NSh-9110.2016.1
The research for this paper was supported by grant NSh-9110.2016.1 "Complex analysis and its applications".


DOI: https://doi.org/10.17516/1997-1397-2018-11-6-776-780

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Bibliographic databases:

UDC: 517.55
Received: 22.12.2017
Received in revised form: 08.09.2018
Accepted: 04.10.2018
Language:

Citation: Maria A. Stepanova, “Jacobian conjecture for mappings of a special type in ${\mathbb C}^2$”, J. Sib. Fed. Univ. Math. Phys., 11:6 (2018), 776–780

Citation in format AMSBIB
\Bibitem{Ste18}
\by Maria~A.~Stepanova
\paper Jacobian conjecture for mappings of a special type in ${\mathbb C}^2$
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2018
\vol 11
\issue 6
\pages 776--780
\mathnet{http://mi.mathnet.ru/jsfu726}
\crossref{https://doi.org/10.17516/1997-1397-2018-11-6-776-780}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000452216700013}


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