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

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

2002-04-25

arxiv.org/abs/nlin/0204059v1

Nonlinear Sciences

Chaotic Dynamics

6 pages, 2 tables

Scientific paper

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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