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Ruelle gave a formula for linear response of transitive Anosovdiffeomorphisms. Recently, practically computable realizations of Ruelle'sformula have emerged that potentially enable sensitivity analysis of certainhigh-dimensional chaotic numerical simulations encountered in the appliedsciences. In this paper, we provide full mathematical justification for theconvergence of one such efficient computation, the space-split sensitivity, orS3, algorithm. In S3, Ruelle's formula is computed as a sum of two termsobtained by decomposing the perturbation vector field into a coboundary and aremainder that is parallel to the unstable direction. Such a decompositionresults in a splitting of Ruelle's formula that is amenable to efficientcomputation. We prove the existence of the S3 decomposition and the convergenceof the computations of both resulting components of Ruelle's formula.

Rigorous justification for the space-split sensitivity algorithm to compute linear response in Anosov systems