Differentiation of SRB states for hyperbolic flows

Let the C³ vector field X+aX on M define a flow ( f a t ) with an Axiom A attractor Λ a depending continuously on a ∈(−ϵ,ϵ). Let ρ a be the SRB measure on Λ a for ( f a t ). If A∈ C²(M) , then a↦ ρ ₐ(A) is C¹ on (−ϵ,ϵ) and dρ a ( A )/ da is the limit when ω →0 with Im ω >0 of