Abstract:
We show that a polynomial mapping of the type (x→F[x+f(a(x)+b(y))],y→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.
\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{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000452216700013}
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This publication is cited in the following 3 articles: