Feigenbaum Fixed Point Hyperbolicity and Golden-Mean Scaling in Siegel Disks — E8 Intelligence Research

FINDING: Feigenbaum renormalization fixed point exhibits hyperbolicity and universality for golden-mean Siegel disks, with golden ratio as the critical scaling factor in quasiperiodic dynamics. | MATH: Golden ratio φ = (1+√5)/2 ≈ 1.618; its reciprocal φ⁻¹ ≈ 0.618; Feigenbaum fixed point δ ≈ 4.6692016 (period-doubling), α ≈ 2.5029079 (scale factor); golden-mean rotation number ω = (√5-1)/2 ≈ 0.618; renormalization operator R acting on function space; Siegel disk boundary scaling by φ. | CONNECTION: Golden ratio φ and its reciprocal 0.618 appear as the universal rotation number for critical circle maps; the Feigenbaum tower's inflexibility links to parabolic domains with rotation numbers related to φ; the golden mean's continued fraction 1;1,1,1,... yields optimal convergence and is the "most irrational" number, central to KAM theory and quasiperiodic order. | DEPTH: 9 — This establishes a rigorous bridge between renormalization group theory (Feigenbaum universality) and quasiperiodic Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com