Abstract
In the paper the equivalence of the constancy of Jacobian of holomorphic mapping in two variables with the pseudoorthogonality of powers of its coordinates is showed. There is also obtained a characterization of holomorphic mapping with the constant Jacobian by one coordinate and the restriction of the other coordinate of the mapping to one of the axes.
Keywords
- Positive Integer
- Holomorphic Mapping
- Inverse Mapping
- Laurent Series
- Positive Power
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Bibliography
Charzyński Z., Chądzyński J., Skibiński P., A contribution to Keller's Jacobian conjecture III, Bull. Soc. Sci. Lettres Łódź, 39 (58) (1989), 1–8.
Щабат Б. В. Бъедение в комплексный анализ, Москва 1969.
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© 1992 Springer-Verlag
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Charzyński, Z., Skibiński, P. (1992). Pseudoorthogonality of powers of the coordinates of a holomorphic mapping in two variables with the constant Jacobian. In: Coste, M., Mahé, L., Roy, MF. (eds) Real Algebraic Geometry. Lecture Notes in Mathematics, vol 1524. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0084619
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DOI: https://doi.org/10.1007/BFb0084619
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-55992-4
Online ISBN: 978-3-540-47337-4
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