Uniqueness of holomorphic Abel functions at a complex fixed point pair

Abstract

We give a simple uniqueness criterion (and some derived criteria) for holomorphic Abel functions and show that Kneser’s real analytic Abel function of the exponential is subject to this criterion.

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Correspondence to Henryk Trappmann.

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Trappmann, H., Kouznetsov, D. Uniqueness of holomorphic Abel functions at a complex fixed point pair. Aequat. Math. 81, 65–76 (2011). https://doi.org/10.1007/s00010-010-0021-6

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Mathematics Subject Classification (2000)

  • Primary 30D05

Keywords

  • Abel function
  • Abel equation
  • exponential function
  • fractional iterates
  • holomorphic solution
  • real analytic