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Maps that are roots of power series

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Abstract

We introduce a class of polynomial maps that we call polynomial roots of powerseries, and show that automorphisms with this property generate the automorphism group in any dimension. In particular we determine generically which polynomial maps that preserve the origin are roots of powerseries. We study the one-dimensional case in greater depth.

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Authors and Affiliations

  1. Department of Mathematics, Radboud Universiteit Nijmegen, Toernooived 1, 6500 GL, Nijmegen, The Netherlands

    Stefan Maubach

  2. Department of Mathematics, University of Wisconsin, 480 Lincoln Drive, Madison, WI, 53706, USA

    Han Peters

Authors
  1. Stefan Maubach
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  2. Han Peters
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Correspondence to Han Peters.

Additional information

Funded by Veni-grant of council for the physical sciences, Netherlands Organisation for scientific research (NWO).

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Maubach, S., Peters, H. Maps that are roots of power series. Math. Z. 259, 903–914 (2008). https://doi.org/10.1007/s00209-007-0255-8

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  • DOI: https://doi.org/10.1007/s00209-007-0255-8

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