We show that the derivative of the transfer operator with respect to perturbations of the map is a divergence. We show that, in high dimensions, approximating singular measures by isotropic finite-elements, and computing the derivative operator on such approximate measures, are both expensive. We show the equivalence between the operator and ensemble version of the linear response formula, and discuss how to combine both formula, as done by the fast linear response algorithm, to reduce cost.

翻译：我们显示,转让操作员在地图扰动方面的衍生物是一个差异。 我们显示,在高维度方面,通过异位有限元素进行近似单一的计量,以及用这种近似计量法计算衍生操作员,两者都是昂贵的。 我们显示了线性响应公式的操作员和组合版本的等值,并讨论了如何像快速线性响应算法那样将两种公式结合起来以降低成本。