Geodesic
Quasi-polynomial mappings with constant Jacobian
Izvestiya. Mathematics , Tome 85 (2021) no. 3, pp. 506-517

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The famous Jacobian conjecture (JC) remains open even for dimension $2$. In this paper we study it by extending the class of polynomial mappings to quasi-polynomial ones. We show that any possible non-invertible polynomial mapping with non-zero constant Jacobian can be transformed into a special reduced form by a sequence of elementary transformations.
Keywords: Newton polynomial, Abhyankar's equation, quasi-polynomial mappings.
Mots-clés : Jacobian conjecture 
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     author = {S. I. Pinchuk},
     title = {Quasi-polynomial mappings with constant {Jacobian}},
     journal = {Izvestiya. Mathematics },
     pages = {506--517},
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     number = {3},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2021_85_3_a10/}
}
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S. I. Pinchuk. Quasi-polynomial mappings with constant Jacobian. Izvestiya. Mathematics , Tome 85 (2021) no. 3, pp. 506-517. http://geodesic.mathdoc.fr/item/IM2_2021_85_3_a10/