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On the existence of fixed points of the composition operator for circle maps

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Abstract

In the theory of circle maps with golden ratio rotation number formulated by Feigenbaum, Kadanoff, and Shenker [FKS], and by Ostlund, Rand, Sethna, and Siggia [ORSS], a central role is played by fixed points of a certain composition operator in map space. We define a common setting for the problem of proving the existence of these fixed points and of those occurring in the theory of maps of the interval. We give a proof of the existence of the fixed points for a wide range of the parameters on which they depend.

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Authors and Affiliations

  1. Département de Physique Théorique, Université de Genève, Bd. d'Yvoy, CH-1211, Genève, Switzerland

    J. -P. Eckmann

  2. Institut des Hautes Etudes Scientifiques, 35 route de Chartres, F-91440, 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. On the existence of fixed points of the composition operator for circle maps. Commun.Math. Phys. 107, 213–231 (1986). https://doi.org/10.1007/BF01209392

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  • DOI: https://doi.org/10.1007/BF01209392

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