= Positive time change of a smooth flow
{title2=$\widetilde F=fF,\ f>0$}
Write $\rho=1/f$ and $t=\int_0^s\rho(\phi_r x)\,dr$. For an <Anosov stable bundle>, the new stable directions are $v+\lambda_s(x,v)F(x)$, where $\lambda_s=\rho(x)^{-1}\int_0^\infty d\rho_{\phi_r x}(D\phi_rv)\,dr$. Exponential contraction makes this integral uniformly convergent. Differentiating the clock equation shows that its flow-direction coefficient after time $t$ is $\rho(\phi_sx)^{-1}\int_s^\infty d\rho(D\phi_rv)\,dr$, which decays exponentially and has the same graph form at the new point. Negative-time integrals give the unstable graph. Compactness and positivity of $f$ compare old and new times uniformly, preserving the <Anosov flow> property.
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