ISSN:
1420-9039
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Physics
Notes:
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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00917874
