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Digitale Medien

Conjugation for polynomial mappings (1995)

Deng, Bo ; Meisters, Gary H. ; Zampieri, Gaetano

Springer

Zeitschrift für angewandte Mathematik und Physik 46 (1995), S. 872-882

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Details

ISSN: 1420-9039

Quelle: Springer Online Journal Archives 1860-2000

Thema: Mathematik , Physik

Notizen: Abstract We consider Keller's functions, namely polynomial functionsf:C n →C n with detf(x)=1 at allx εC n. Keller conjectured that they are all bijective and have polynomial inverses. The problem is still open. Without loss of generality assumef(0)=0 andf'(0)=I. We study the existence of certain mappingsh λ, λ 〉 1, defined by power series in a ball with center at the origin, such thath′λ(0)=I andh λ(λf(x))=λh λ(x). So eachh λ conjugates λf to its linear part λI in a ball where it is injective. We conjecture that for Keller's functionsf of the homogeneous formf(x)=x +g(x),g(sx)=s dg(x),g′(x)n=0,xεC n,sεC the conjugationh λ for λf is anentire function.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1007/BF00917874

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