Gaussian thermostat
= Gaussian thermostat
{c}
{title2=$D_t\dot\gamma=E-\langle E,\dot\gamma\rangle\dot\gamma$}
At unit speed on a <Riemannian surface>, the right-hand side is $\langle E,iv\rangle iv$. This removes the velocity-parallel component of the forcing, so differentiating $|\dot\gamma|^2$ gives zero. The dynamics need not preserve the ordinary <Liouville volume of a surface geodesic flow>.