= Generalized thermostat on a Riemannian surface
{title2=$F=X+\lambda V,\qquad D_t\dot\gamma=\lambda(\gamma,\dot\gamma)i\dot\gamma$}
= Surface thermostat
{synonym}
A smooth real function $\lambda$ on the <unit tangent bundle> determines this unit-speed <smooth flow>. Its base velocity is $v$, so its generator never vanishes. In the canonical frame its divergence in <Liouville volume of a surface geodesic flow> is $V\lambda$. The special case where $\lambda$ depends only on the base is a <magnetic flow>; when $\lambda(x,v)=\langle E(x),iv\rangle$ it is a <Gaussian thermostat>.
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