Power-law divergence of nearby trajectories on the Feigenbaum attractor is discussed in terms of the algebraic index β. A statistical analysis is performed by following a multifractal approach. As a result, a fluctuating spectrum h(β) is found, whose complete characterization requires the introduction of a generalized "multispectral" analysis. A simple model of period-doubling is extensively discussed, allowing to clarify many details of the related problems. A similar approach is expected to work in generic transitions towards chaotic behaviour.
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Anania et al. (1988) studied this question.
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