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Real Jacobian mates

Volume 117 / 2016

Janusz Gwoździewicz Annales Polonici Mathematici 117 (2016), 207-213 MSC: Primary 14R15; Secondary 14R25. DOI: 10.4064/ap3740-8-2016 Published online: 9 September 2016


Let $p$ be a real polynomial in two variables. We say that a polynomial $q$ is a real Jacobian mate of $p$ if the Jacobian determinant of the mapping $(p,q):\mathbb {R}^2\to \mathbb {R}^2$ vanishes nowhere. We present a class of polynomials that do not have real Jacobian mates.


  • Janusz GwoździewiczInstitute of Mathematics
    Pedagogical University of Cracow
    Podchorążych 2
    30-084 Kraków, Poland

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