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The zero diffusion limit of 2-D Navier-Stokes equations with $L^1$ initial vorticity
On two noteworthy deformations of negatively curved Riemannian metrics
1. | Centro de Matemática, Facultad de Ciencias, Iguá 4225, 11400 Montevideo, Uruguay |
$L_\lambda (x, v) =\frac{1}{2}|v|^2_x-\lambda\theta_x(v),$
and let $h_F(\lambda)$ be the topological entropy of the geodesic flow of the Finsler metric,
$F_\lambda(x, v) = |v|_x-\lambda\theta_x(v),$
We show that $h_{E L}''(0) + h''_F(0) = h^2$Var$(\theta)$, where Var$(\theta)$ is the variance of $\theta$ with respect to the measure of maximal entropy of $\phi$ and $h$ is the topological entropy of $\phi$. We derive various consequences from this formula.
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