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arXiv · 2607.18771

Statistical periodicity in noise-induced order from Ruelle-Pollicott resonances

Yuzuru Sato·Isaia Nisoli
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Abstract

Noise-induced order (NIO) is a paradigmatic example of nontrivial noise-induced phenomena, characterized by pronounced spectral peaks and pseudoperiodic dynamics. We show that this periodicity is governed by the Ruelle-Pollicott resonances of the annealed transfer operator, independently of dynamical stability. Exact results for an analytically solvable model and numerical results for a modified Lasota--Mackey map show excellent agreement between resonance-based predictions and empirical power spectra across a broad range of noise amplitudes. Independent transitions in stability, diagnosed by the Lyapunov exponent, and statistical periodicity, diagnosed by the Ruelle-Pollicott resonances, give rise to three distinct types of NIO.

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Yuzuru Sato, Isaia Nisoli. 2026-07-21. Statistical periodicity in noise-induced order from Ruelle-Pollicott resonances. https://arxiv.org/abs/2607.18771

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