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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https://www.mathnet.ru/eng/jsfu726
https://www.mathnet.ru/eng/jsfu/v11/i6/p776
This publication is cited in the following 3 articles:
T. M. SADYKOV, “A PACKAGE OF PROCEDURES AND FUNCTIONS FOR CONSTRUCTIONS AND INVERSION OF ANALYTIC MAPPINGS WITH UNIT JACOBIAN”, Programmirovanie, 2023, no. 1, 61
Timur Sadykov, “Parameterizing and inverting analytic mappings with unit Jacobian”, Mosc. Math. J., 23:3 (2023), 369–400
V. A. Krasikov, “Analytic complexity of hypergeometric functions satisfying systems with holonomic rank two”, Computer Algebra in Scientific Computing (Casc 2019), Lecture Notes in Computer Science, 11661, eds. M. England, W. Koepf, T. Sadykov, W. Seiler, E. Vorozhtsov, Springer, 2019, 330–342
Citation in format AMSBIB
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