Under minimal Kahane–Peyrière integrability, the Fourier dimension of a scalar dyadic Mandelbrot cascade pushed onto any fixed nondegenerate C² arc or Jordan curve equals A_loc(W), the same explicit endpoint value as the canonical circle.
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Under minimal Kahane-Peyriere integrability, dyadic Mandelbrot cascades satisfy dim_F(mu) = dim_E(mu) = dim_2(mu) = D_E(X) almost surely on non-extinction, with explicit sup formulas for scalar and circle cases.
Fourier dimension of canonical Mandelbrot cascade measures equals the energy exponent almost surely under the minimal Kahane-Peyrière integrability condition.
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Exact Fourier dimensions of dyadic Mandelbrot cascades on curves of nonvanishing curvature under minimal integrability
Under minimal Kahane–Peyrière integrability, the Fourier dimension of a scalar dyadic Mandelbrot cascade pushed onto any fixed nondegenerate C² arc or Jordan curve equals A_loc(W), the same explicit endpoint value as the canonical circle.
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Exact Fourier dimensions of dyadic Mandelbrot cascades under minimal integrability
Under minimal Kahane-Peyriere integrability, dyadic Mandelbrot cascades satisfy dim_F(mu) = dim_E(mu) = dim_2(mu) = D_E(X) almost surely on non-extinction, with explicit sup formulas for scalar and circle cases.
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Fourier Dimensions of Mandelbrot Cascades under Minimal Integrability
Fourier dimension of canonical Mandelbrot cascade measures equals the energy exponent almost surely under the minimal Kahane-Peyrière integrability condition.