04-246 D. Ruelle
Differentiation of SRB states for hyperbolic flows. (54K, plain TeX) Aug 6, 04
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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 $$\int_0^\infty e^{i\omega t}dt \int\rho_a(dx)\,X(x)\cdot\nabla_x(A\circ f_a^t)$$

Files: 04-246.src( 04-246.keywords , flows.tex )