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

Understand

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.