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A computable realization of Ruelle's formula for linear response of statistics in chaotic systems

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arxiv 2002.04117 v3 pith:JGUYVNA7 submitted 2020-02-10 math.DS math-phmath.MPnlin.CD

classification math.DSmath-phmath.MPnlin.CD
keywords formulasensitivitychaoticcomputablehyperboliclinearpointsreformulation
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abstract

We present a computable reformulation of Ruelle's linear response formula for chaotic systems. The new formula, called Space-Split Sensitivity or S3, achieves an error convergence of the order ${\cal O}(1/\sqrt{N})$ using $N$ phase points. The reformulation is based on splitting the overall sensitivity into that to stable and unstable components of the perturbation. The unstable contribution to the sensitivity is regularized using ergodic properties and the hyperbolic structure of the dynamics. Numerical examples of uniformly hyperbolic attractors are used to validate the S3 formula against a na\"ive finite-difference calculation; sensitivities match closely, with far fewer sample points required by S3.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. A Mathematical Framework for Linear Response Theory for Nonautonomous Systems

    math.DS 2026-03 unverdicted novelty 8.0 of 10

    Under uniform Lasota–Yorke bounds, differentiability of the cocycle, and exponential loss of memory, the equivariant measure family of a nonautonomous system is differentiable in the weak topology with an explicit Neu...

  2. Interpretable and Equation-Free Response Theory for Complex Systems

    cond-mat.stat-mech 2025-02 conditional novelty 6.0 of 10

    For Markov chains, linear and nonlinear response to time-dependent forcings can be written as sums of exponentials governed by the chain's Koopman eigenvalues, enabling equation-free response prediction.

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