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On the Existence of Global Analytic Conjugations for Polynomial Mappings of Yagzhev Type

By Gianluca Gorni and Gaetano Zampieri

Abstract

AbstractConsider a mappingf:Cn→Cnof the form identity plus a term with polynomial components that are homogeneous of the third degree, and suppose that the Jacobian determinant of this mapping is constant throughout Cn(polynomial mapping of Yagzhev type). As a stronger version of the classical Jacobian conjecture, the question has been posed whether for some values of λ∈C\{0} there exists a global change of variables (“conjugation”) on Cnthrough which the mapping λfbecomes its linear part at the origin. Van den Essen has recently produced a simple Yagzhev mapping for which no suchpolynomialconjugation exists. We show here that van den Essen's example still admitsglobal analyticconjugations. The question on the existence of global conjugations for general Yagzhev maps is then still open

Publisher: Academic Press.
Year: 1996
DOI identifier: 10.1006/jmaa.1996.0290
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