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Generalized dimensions of Feigenbaum's attractor from renormalization-group functional equations

S. P. Kuznetsov·A. H. Osbaldestin
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Abstract

A method is suggested for the computation of the generalized dimensions of fractal attractors at the period-doubling transition to chaos. The approach is based on an eigenvalue problem formulated in terms of functional equations, with a coefficient expressed in terms of Feigenbaum's universal fixed-point function. The accuracy of the results is determined only by precision of the representation of the universal function.

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S. P. Kuznetsov, A. H. Osbaldestin. 2002-04-25. Generalized dimensions of Feigenbaum's attractor from renormalization-group functional equations. https://arxiv.org/abs/nlin/0204059

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