Conjugation for polynomial mappings

Bo Deng, Gary H. Meisters, Gaetano Zampieri

Research output: Contribution to journalArticle

7 Scopus citations

Abstract

We consider Keller's functions, namely polynomial functions f:Cn →Cn with det f(x)=1 at all x εCn. Keller conjectured that they are all bijective and have polynomial inverses. The problem is still open. Without loss of generality assume f(0)=0 and f'(0)=I. We study the existence of certain mappings hλ, λ > 1, defined by power series in a ball with center at the origin, such that h′λ(0)=I and hλ(λf(x))=λhλ(x). So each hλconjugates λf to its linear part λI in a ball where it is injective. We conjecture that for Keller's functions f of the homogeneous form f(x)=x +g(x), g(sx)=sdg(x), g′(x)n=0, xεCn, sεC the conjugation hλ for λf is an entire function.

Original languageEnglish (US)
Pages (from-to)872-882
Number of pages11
JournalZAMP Zeitschrift für angewandte Mathematik und Physik
Volume46
Issue number6
DOIs
StatePublished - Nov 1 1995

ASJC Scopus subject areas

  • Mathematics(all)
  • Physics and Astronomy(all)
  • Applied Mathematics

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