Abstract
The theory of period doublings for one-parameter families of iterated real mappings is generalized to periodn-tuplings for complex mappings. Ann-tupling occurs when the eigenvalue of a stable periodic orbit passes through the value ω=exp(2πim/n) as the parameter value is changed. Each choice ofm defines a different sequence ofn-tuplings, for which we construct a periodn-tupling renormalization operator with a universal fixpoint function, a universal unstable manifold and universal scaling numbers. These scaling numbers can be organized by Farey trees. The present paper gives a general description and numerical support for the universality conjectured above.
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Communicated by J.-P. Eckmann
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Cvitanović, P., Myrheim, J. Complex universality. Commun.Math. Phys. 121, 225–254 (1989). https://doi.org/10.1007/BF01217804
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DOI: https://doi.org/10.1007/BF01217804