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Izvestiya: Mathematics, 2021, Volume 85, Issue 3, Pages 506–517
DOI: https://doi.org/10.1070/IM9017 (Mi im9017) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Quasi-polynomial mappings with constant Jacobian

S. I. Pinchuk

Department of Mathematics, Indiana University, Bloomington, IN, USA
English version PDF (466 kB) Citations (1) Russian version article
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DOI: https://doi.org/10.1070/IM9017
Abstract: 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: Jacobian conjecture, Newton polynomial, Abhyankar's equation, quasi-polynomial mappings.
Received: 03.02.2020
Revised: 14.07.2020
Bibliographic databases:
Document Type: Article
UDC: 512.76+512.774+514.763.8
MSC: 14R15, 13R20
Language: English
Original paper language: Russian
Citation: S. I. Pinchuk, “Quasi-polynomial mappings with constant Jacobian”, Izv. Math., 85:3 (2021), 506–517
Citation in format AMSBIB
\Bibitem{Pin21}
\by S.~I.~Pinchuk
\paper Quasi-polynomial mappings with constant Jacobian
\jour Izv. Math.
\yr 2021
\vol 85
\issue 3
\pages 506--517
\mathnet{http://mi.mathnet.ru//eng/im9017}
\crossref{https://doi.org/10.1070/IM9017}
\zmath{https://zbmath.org/?q=an:1471.14125}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2021IzMat..85..506P}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000671434500001}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85110478778}
Linking options:
  • https://www.mathnet.ru/eng/im9017
  • https://doi.org/10.1070/IM9017
  • https://www.mathnet.ru/eng/im/v85/i3/p178
    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:274
    Russian version PDF:51
    English version PDF:56
    Russian version HTML:107
    References:39
    First page:19
     
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