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March 22, 2026Open Access

Universal area-decay exponents in K-parameterized non-holomorphic iterations

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Authors

MBMichael Bird

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Overview

This analysis demonstrates universal area-decay exponents in K-parameterized non-holomorphic iterations, indicating novel classification methods.

Key Points

  • The research aims to investigate the behavior of non-holomorphic complex iterations and classify their stability properties based on parameters.
  • Study of the family of non-holomorphic iterations defined by zn+1 = Kzng(Im(zn))+c.
  • Proof of an exact Decoupling Lemma and derivation of a two-step stability boundary.
  • Analysis of stability parameter-space area A(K) with respect to the vanishing order α of function g.
  • Identification of three universality classes (A, B, and C) based on the behavior of the function g.
  • Verification of predicted exponents with high precision across multiple functions from various scientific fields.
  • Proof of the formula γ = 2/(1 + α) for certain values of α and derivation of constants involving Euler Beta functions.

Cite This Study

Michael Bird (2026) studied this question.

synapsesocial.com/papers/69bf898bf665edcd009e93bchttps://doi.org/10.5281/zenodo.19116017
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