For discrete time systems, we show that the derivative of the (measure) transfer operator with respect to the system parameters is a divergence. Then, for physical measures of hyperbolic chaotic systems, we derive an equivariant divergence formula for the unstable derivative of transfer operators. This formula and hence the derivative of physical measures can be sampled by only $2u+1$ recursive relations on one orbit, where $u$ is the unstable dimension. The numerical implementation of this formula in \cite{arxiv:2111.07692} is neither cursed by dimensionality nor the butterfly effect.

翻译：对于离散时间系统,我们显示,(量度)转移操作器相对于系统参数的衍生物是差异的。然后,对于双曲混杂系统的物理测量,我们为转移操作器的不稳定衍生物得出一个等同的差异公式。这个公式以及因此产生的物理测量的衍生物只能通过一个轨道上的二次关系进行抽样,一个轨道上的循环关系是1美元,其中美元是不稳定的维度。这个公式在\cite{arxiv:21111.07692}中的数值执行既没有受到维度的诅咒,也没有受到蝴蝶效应的诅咒。