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Bounds on the unstable eigenvalue for period doubling

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Abstract

Bounds are given for the unstable eigenvalue of the period-doubling operator for unimodal maps of the interval. These bounds hold for all types of behaviour |x|r of the interval map near its critical point. They are obtained by finding cones in function space which are invariant under the tangent map to the doubling operator at its fixed point.

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Authors and Affiliations

  1. Département de Physique Théorique, Université de Genève, CH-1211, Genève 4, Switzerland

    J. -P. Eckmann

  2. CNRS and IHES, Bures sur Yvette, France

    H. Epstein

Authors
  1. J. -P. Eckmann
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  2. H. Epstein
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Communicated by A. Jaffe

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Eckmann, J.P., Epstein, H. Bounds on the unstable eigenvalue for period doubling. Commun.Math. Phys. 128, 427–435 (1990). https://doi.org/10.1007/BF02108789

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  • DOI: https://doi.org/10.1007/BF02108789

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