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

✍ Scribed by Gianluca Gorni; Gaetano Zampieri

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
184 KB
Volume
201
Category
Article
ISSN
0022-247X

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✦ Synopsis

DEDICATED TO LUIGI SALVADORI ON THE OCCASION OF HIS 70TH BIRTHDAY

Consider a mapping f : ‫ރ‬ n Βͺ ‫ރ‬ n of the form identity plus a term with polynomial components that are homogeneous of the third degree, and suppose that the n Ε½ Jacobian determinant of this mapping is constant throughout ‫ރ‬ polynomial . mapping of Yagzhev type . As a stronger version of the classical Jacobian conjec-Γ„ 4 ture, the question has been posed whether for some values of g ‫ރ‬ _ 0 there Ε½ .

n exists a global change of variables ''conjugation'' on ‫ރ‬ through which the mapping f becomes its linear part at the origin. Van den Essen has recently produced a simple Yagzhev mapping for which no such polynomial conjugation exists. We show here that van den Essen's example still admits global analytic conjugations. The question on the existence of global conjugations for general Yagzhev maps is then still open.

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