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Bounds on the Unstable Eigenvalue for the Asymmetric Renormalization Operator for Period Doubling

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Abstract

We establish rigorous bounds for the unstable eigenvalue of the period-doubling renormalization operator for asymmetric unimodal maps. Herglotz-function techniques and cone invariance ideas are used. Our result generalizes an established result for conventional period doubling.

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Authors and Affiliations

  1. Department of Computing Science and Mathematics, University of Stirling, Stirling, FK9 4LA, UK

    B.D. Mestel

  2. Department of Mathematics, University of Portsmouth, Portsmouth, PO1 3HE, UK

    A.H. Osbaldestin

  3. Unite de Mathématiques, Pures et Appliquées, Ecole Normale Supérieure de Lyon, 46 Allée d’Italie, 69364, Lyon Cedex 07, France

    A.V. Tsygvintsev

Authors
  1. B.D. Mestel
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  2. A.H. Osbaldestin
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  3. A.V. Tsygvintsev
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Correspondence to B.D. Mestel.

Additional information

Communicated by G. Gallavotti

This research is supported by The Leverhulme Trust (grant number F/00144/W).

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Mestel, B., Osbaldestin, A. & Tsygvintsev, A. Bounds on the Unstable Eigenvalue for the Asymmetric Renormalization Operator for Period Doubling. Commun. Math. Phys. 250, 241–257 (2004). https://doi.org/10.1007/s00220-004-1143-2

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  • DOI: https://doi.org/10.1007/s00220-004-1143-2

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