D. Ruelle
Differentiation of SRB states for hyperbolic flows.
(54K, plain TeX)

ABSTRACT.  Let the ${\cal C}^3$ vector field ${\cal X}+aX$ on $M$ define a flow $(f^t_a)$ with an Axiom A attractor $\Lambda_a$ depending continuously on $a\in(-\epsilon,\epsilon)$. Let $\rho_a$ be the SRB measure on $\Lambda_a$ for $(f^t_a)$. If $A\in{\cal C}^2(M)$, then $a\mapsto\rho_a(A)$ is ${\cal C}^1$ on $(-\epsilon,\epsilon)$ and $d\rho_a(A)/da$ is the limit when $\omega\to0$ with ${\rm Im}\omega>0$ of 
$$ \int_0^\infty e^{i\omega t}dt 
 \int\rho_a(dx)\,X(x)\cdot\nabla_x(A\circ f_a^t) $$