This analysis classifies universality in fractal dynamics, demonstrating stability boundaries and decoupling in non-holomorphic iterations.
Key Points
The aim is to classify non-holomorphic complex iterations and identify universal area-decay exponents related to parameter conditions.
Derived an exact Decoupling Lemma for complex iterations.
Established a closed-form two-step stability boundary.
Characterized three universality classes based on the vanishing order of gate functions.
Verified predictions across eight functions within various scientific fields.
Identified universal decay exponents γ for three distinct classes: Class A (γ=2), Class B (γ=1 with logarithmic correction), and Class C (anomalous scaling).
Validated the formula γ=2/(1 + α) for 0 < α ≤1 and γ=1/α for α>1.
Observed a sharp phase transition at K* ≈ 25, leading to distinct power-law and exponential-collapse behaviors.