  Sensitivity analysis in chaotic dynamical systems is a challenging task from
a computational point of view. In this work, we present a numerical
investigation of a novel approach, known as the space-split sensitivity or S3
algorithm. The S3 algorithm is an ergodic-averaging method to differentiate
statistics in ergodic, chaotic systems, rigorously based on the theory of
hyperbolic dynamics. We illustrate S3 on one-dimensional chaotic maps,
revealing its computational advantage over naive finite difference computations
of the same statistical response. In addition, we provide an intuitive
explanation of the key components of the S3 algorithm, including the density
gradient function.

Chaotic Dynamics