Fixed Points III: Disturbance - Damping Balance and Stability

Zenodo (CERN European Organization for Nuclear Research) 2026 Preprint Open access

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Authors: Peter Nero
DOI: 10.5281/zenodo.18202941
Cited by: 0

Abstract

We extend the fixed-point framework to stochastic disturbances and damping balance. Each non-harmonic mode obeys an Ornstein–Uhlenbeck equation da = −γ a dt + √δ dW_t. We prove that if γ > 0 then Var(a) tends to δ/(2γ), establishing finite stationary variance. Bundlewise stability is guaranteed by summability of δ/(1+λ). This provides a rigorous criterion for stability under persistent stochastic forcing in the coherent sector.

Fields of Study & Subjects

Nonlinear Dynamics and Pattern Formation Complex Systems and Dynamics Mathematical Dynamics and Fractals

Publication details

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