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  • 1995-1999  (2)
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Material
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Year
  • 1
    Electronic Resource
    Electronic Resource
    Conjugation for polynomial mappings (1995)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 46 (1995), S. 872-882 
    Details
    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
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Local extrema of analytic functions (1996)
    Springer
    Nonlinear differential equations and applications 3 (1996), S. 287-303 
    Details
    ISSN: 1420-9004
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We give a complete answer to the problem of the finite decidability of the local extremality character of a real analytic function at a given point, a problem that found partial answers in some works by Severi and Łojasiewicz. Consider a real analytic functionf defined in a neighbourhood of a pointx 0∈R n . Restrictf to the spherical surface centered inx 0 and with radiusr≥0 and take its infimumm(r) and its supremumM(r). We establish some properties ofm(r) andM(r) for smallr〉0. In particular, we prove that they have asymptotic expansions of the formf(x 0)+c·(r α+o(r α)) asr→0 for a realc and a rational α≥1 (of course the parameters will usually be different form andM).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01194068
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
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