Borel-Plane Probes at the Aether Limit: Extended Negative Atlas for the Non-Holomorphic Bird Map (Paper 21 in the Non-Holomorphic Fractal Series)

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Authors: Michael Bird
Cited by: 12
References: 4

Abstract

Paper 21 in the Non-Holomorphic Fractal Series. Papers 18–20 established a calibrated negative atlas for the non-holomorphic Bird map at finite C = 0.3605: the orbit-multiplier, Watson–Borel (WBA), and alien-strength ladders all show no Padé-stable, N-stable real-axis singularity in the Feigenbaum window [0.85, 1.15] under the calibrated gamma-family Padé–Borel skeleton, even after first-order alien correction. We now extend this atlas to the Aether limit (α → ∞) of the Bird map, feeding the Aether-limit orbit-multiplier slope ladder (500 terms) into a direct clone of the Paper 20 gamma-family driver. The G4 synthetic calibration reproduces the Paper 19/20 fingerprint exactly: a planted pole at s₀ = 0.19013 maps to s̃ ≈ 0.9995 (stable across all N ∈ {40, 60, 80} and Padé slices, 8/8 hits). Against real Aether data, no Padé-stable, N-stable singularity is found in the Feigenbaum window for any σ ∈ {1, 2, 5.263, 10}, either with or without first-order global-scale alien correction. At the Aether limit the Feigenbaum pole remains invisible to the calibrated gamma-family Padé–Borel probe at N ≤ 80, extending the negative atlas from finite-C Class C to the infinite-α regime.

Fields of Study & Subjects

Mathematical Dynamics and Fractals Chaos control and synchronization Quantum chaos and dynamical systems

Publication details

Journal / source
Zenodo (CERN European Organization for Nuclear Research)
Publication date
30 March 2026
Language
EN
Document type
Preprint