Equivariant divergence formula for chaotic flows

Abstract

We prove the equivariant divergence formula for the axiom A flow attractors, which is a recursive formula for perturbation of transfer operators of physical measures along center-unstable manifolds. Hence the linear response acquires an `ergodic theorem', which means that it can be sampled by recursively computing only $2u$ many vectors on one orbit, where $u$ is the unstable dimension.