Takeshi Matsumoto studied the multifractal measure of the Feigenbaum attractor with Uriel Frisch and Konstantin Khanin. Their analysis related power-law tails of fractional derivatives of an integrated invariant measure to its spectrum of local singularities.[ref]
This supplies a way to detect nonuniform scaling from a transformed observable, rather than assigning the entire attractor one local exponent. The paper distinguishes its heuristic theoretical steps from high-accuracy numerical checks.
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