Geodesic
Jacobian conjecture for mappings of a special type in ${\mathbb C}^2$
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 11 (2018) no. 6, pp. 776-780.

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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. 
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Maria A. Stepanova. Jacobian conjecture for mappings of a special type in ${\mathbb C}^2$. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 11 (2018) no. 6, pp. 776-780. http://geodesic.mathdoc.fr/item/JSFU_2018_11_6_a12/

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