Abstract
Existence and hyperbolicity of fixed points for the mapN p :f(x) →λ−1 f p(λx), withf p p-fold iteration and λ=f p(0) are given forp large. These fixed points come close to being quadratic functions, and our proof consists in controlling perturbation theory about quadratic functions.
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Communicated by O. E. Lanford
Supported in part by the Swiss National Science Foundation
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Eckmann, J.P., Epstein, H. & Wittwer, P. Fixed points of Feigenbaum's type for the equationf p(λx)≡λf(x). Commun.Math. Phys. 93, 495–516 (1984). https://doi.org/10.1007/BF01212292
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DOI: https://doi.org/10.1007/BF01212292