Abstract
We propose an analytic perturbative approach for the determination of the Feigenbaum-Cvitanović function and the universal parameterα occurring in the Feigenbaum scenario of period doubling for approach to chaotic behaviour. We apply the method to the caseZ=2 whereZ is the order of the unique local maximum of the nonlinear map. Our third order approximation givesα=2.5000 as compared to “exact” numerical valueα=2.5029 ... We also obtain a reasonably accurate value of the Feigenbaum-Cvitanović function.
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Singh, V. On the Feigenbaum-Cvitanović equation in the theory of chaotic behaviour. Pramana - J Phys 24, 31–37 (1985). https://doi.org/10.1007/BF02894814
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DOI: https://doi.org/10.1007/BF02894814