Abstract
The universal map for the period-doubling transition to chaos is studied numerically in the complex plane. The boundary of the domain of analyticity of this function is obtained graphically and is shown to be a fractal with self-similar properties obtained by rescaling with the universal constantsα andδ. In the complex parameter plane, this domain is shown asymptotically to be similar to part of the Mandelbrot set.
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Nauenberg, M. Fractal boundary of domain of analyticity of the Feigenbaum function and relation to the Mandelbrot set. J Stat Phys 47, 459–475 (1987). https://doi.org/10.1007/BF01007520
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DOI: https://doi.org/10.1007/BF01007520