Moscow University Physics Bulletin

, Volume 65, Issue 2, pp 91–98 | Cite as

Holomorphic extension of the logistic sequence

Article

Abstract

The logistic problem is formulated in terms of the Superfunction and Abelfunction of the quadratic transfer function H(z) = uz(1 − z). The Superfunction F as holomorphic solution of equation H(F(z)) = F(z + 1) generalizes the logistic sequence to the complex values of the argument z. The efficient algorithm for the evaluation of function F and its inverse function, id est, the Abelfunction G are suggested; F(G(z)) = z. The halfiteration h(z) = F(1/2 + G(z)) is constructed; in wide range of values z, the relation h(h(z)) = H(z) holds. For the special case u = 4, the Superfunction F and the Abelfunction G are expressed in terms of elementary functions.

Key words

Logistic operator Logistic sequence Holomorphic extension Superfunction Abelfunction Pomeau-Manneville scenario 

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Copyright information

© Allerton Press, Inc. 2010

Authors and Affiliations

  1. 1.Institute for Laser ScienceUniversity of Electro-CommunicationsTokyoJapan

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