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On the existence of Feigenbaum's fixed point

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Abstract

We give a proof of the existence of aC 2, even solution of Feigenbaum's functional equation

$$g{\text{(}}x) = - \lambda _0^{ - 1} g{\text{(}}g( - \lambda _0 x)),g{\text{(0) = 1,}}$$

whereg is a map of [−1, 1] into itself. It extends to a real analytic function over ℝ.

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Author notes

  1. M. Campanino

    Present address: Istituto Matematico “G. Castelnuovo”, Università degli studi di Roma, Piazzale A. Moro, I-00100, Roma, Italy

Authors and Affiliations

  1. Institut des Hautes Etudes Scientifiques, F-91440, Bures-sur-Yvette, France

    M. Campanino & H. Epstein

Authors
  1. M. Campanino
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  2. H. Epstein
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Communicated by D. Ruelle

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Campanino, M., Epstein, H. On the existence of Feigenbaum's fixed point. Commun.Math. Phys. 79, 261–302 (1981). https://doi.org/10.1007/BF01942063

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  • DOI: https://doi.org/10.1007/BF01942063

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