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

Abstract Ruelle (1997 Commun. Math. Phys. 187 227–41; 2003 234 185–90) (see also Jiang 2012 Ergod. Theor. Dynam. Syst. 32 1350–69) gave a formula for linear response of transitive Anosov diffeomorphisms. Recently, practically computable realizations Ruelle’s have emerged that potentially enable sensitivity analysis certain high-dimensional chaotic numerical simulations encountered in the applied sciences. In this paper, we provide full mathematical justification convergence one such efficient computation, space–split sensitivity, or S3, algorithm (Chandramoorthy and Wang 2022 SIAM J. Appl. Dyn. 21 735–81). is computed as sum two terms obtained by decomposing perturbation vector field into coboundary remainder parallel to unstable direction. Such decomposition results splitting amenable computation. We prove existence S3 computations both resulting components formula.