Space-split algorithm for sensitivity analysis of discrete chaotic systems with unstable manifolds of arbitrary dimension

The paper derives the S3 splitting, handles the stable term via a constrained tangent recursion with O(N^{-1/2}) Monte Carlo convergence (with a log log N factor) and treats the unstable term by leafwise integration by parts after disintegration, introducing b(i,j) and g^i; it then states (citing earlier work) the quantitative error bound |error| ≤ C1 K/√N + C2 e^{-C3 K} for the truncated estimator and proves exponential forgetting of initialization for all recursions. These match the model’s steps and bounds. Concretely: Ruelle’s formula and S3 split (Eq. (3), (7)–(11)), the stable O(N^{-1/2}) estimate (Eq. (12)), the disintegration and integration by parts with vanishing boundary term and the definitions of b(i,j), g^i (Eq. (15)–(16)), the explicit measure-based QR formula for g^i (Eq. (18)–(20)), the truncated triple-sum estimator (Eq. (37)) and the key inequality (38): C1 K/√N + C2 exp(−C3 K), and the exponential convergence of all auxiliary recursions independent of initialization (Eq. (36) and concluding text). All of these appear in the paper and are exactly what the model leverages. The only nuance is that the paper cites prior work for the full rigorous proof of (38) and emphasizes the order of limits N→∞ then K→∞; the model’s argument is consistent with this and uses standard spectral-gap/ASIP tools to reach the same bounds. Overall, the approaches and conclusions coincide.