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This article is cited in 3 scientific papers (total in 3 papers)
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.
Received: 22.12.2017 Received in revised form: 08.09.2018 Accepted: 04.10.2018
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
Linking options:
https://www.mathnet.ru/eng/jsfu726 https://www.mathnet.ru/eng/jsfu/v11/i6/p776
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Abstract page: | 154 | Full-text PDF : | 72 | References: | 19 |
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