Differentiation of SRB states for hyperbolic flows

Let the ${\cal C}^3$ vector field ${\cal X}+aX$ on M define a flow (fat) with an Axiom A attractor Λa depending continuously on a∈(−ϵ,ϵ). Let ρa be the SRB measure on Λa for (fat). If $A\in {\cal C}^2(M)$, then $a\mapsto \rho _a(A)$ is ${\cal C}^1$ on (−ϵ,ϵ) and dρa(A)/da is the limit when ω→0 with Im ω>0 of