Universal Constants of Period-Doubling: Feigenbaum's δ and α via Renormalization — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: FINDING: Feigenbaum's δ (4.6692…) and α (2.5029…) are universal constants governing period-doubling cascades, derived via renormalization-group fixed points in function space, independent of the specific map. | MATH: δ = lim_{n→∞} (r_{n+1} − r_n)/(r_{n+2} − r_{n+1}) ≈ 4.669201609…; α = lim_{n→∞} (d_n / d_{n+1}) ≈ 2.502907875…; universal function g(x) satisfies renormalization equation g(x) = −α·g(g(x/α)), with g(0)=1, g'(0)=0; logistic map x_{n+1} = r·x_n(1−x_n) exhibits cascade at r_∞ ≈ 3.569945…; Feigenbaum fixed point is hyperbolic (arXiv:math/0301118v1). | CONNECTION: δ ≈ 4.669 ≠ 4.618 (2.618+2.000) — no direct golden-ratio link; however, α ≈ 2.5029 is close to 2.5 (half of 5), and the universal function's scaling ratio α² ≈ 6.2645 ≈ 2π (within 0.3% — notable but not exact). The renormalization group structure mirrors self-similarity found in crystallographic lattices (scale invariance at critical points), but no explicit 0.382/0.618/0.786/1.618/2.618 or base-60 appears in the Feig Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Author: Caldin, Andrew Stewart
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7219750016
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