Equivariant Divergence Formula for Hyperbolic Chaotic Flows

Abstract

We prove the equivariant divergence formula for axiom A flow attractors. It is a pointwisely-defined and recursive formula for perturbation of SRB measures along center-unstable manifolds. It depends on only the zeroth and first order derivatives of the map, the observable, and the perturbation. Hence, the linear response acquires an ‘ergodic theorem’, which means that it can be sampled by recursively computing a few vectors on one orbit.