Uriel Frisch studied nonuniform scaling of invariant measures with Konstantin Khanin and Takeshi Matsumoto. Their work on the Feigenbaum attractor related the statistics of fractional derivatives to the local singularity structure of a multifractal measure.[ref]
A single fractal dimension need not describe how probability concentrates differently from point to point. The derivative-based test offers another way to probe that spatially varying scaling, with the paper explicitly comparing heuristic arguments and precise numerical calculations.
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Uriel Frisch is a prominent astrophysicist known for his contributions to various fields within astrophysics, particularly in cosmology and turbulence. He has been involved in research related to the large-scale structure of the universe, as well as the dynamics and evolution of galaxies and interstellar matter. Additionally, he is known for his work on numerical simulations and theoretical models that help in understanding complex astrophysical phenomena. His academic and research contributions have been influential in advancing the field.