Generalized dimensions of Feigenbaum's attractor from renormalization-group functional equations
S. P. Kuznetsov, A. H. Osbaldestin
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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