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

arXiv2002.04117MaRDI QIDQ6334535

Qiqi Wang, Nisha Chandramoorthy

Publication date: 10 February 2020

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 $calO(1/sqrtN)$ 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.

Has companion code repository: https://github.com/nishaChandramoorthy/s3

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