Differentiation of SRB states for hyperbolic flows
Ruelle, David
HAL, hal-00126394 / Harvested from HAL
Text on HAL
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 $$ \int_0^\infty e^{i\omega t}dt \int\rho_a(dx) X(x)\cdot\nabla_x(A\circ f_a^t) $$
Publié le : 2004-07-05
Classification:  [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS] 
@article{hal-00126394,
     author = {Ruelle, David},
     title = {Differentiation of SRB states for hyperbolic flows},
     journal = {HAL},
     volume = {2004},
     number = {0},
     year = {2004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00126394}
}

Ruelle, David. Differentiation of SRB states for hyperbolic flows. HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/hal-00126394/