Flow coboundary
= Flow coboundary
{title2=$h=Fu$}
A smooth function $h$ is a flow coboundary if $h=Fu$ for some smooth function $u$, where $F$ is the flow generator. Equivalently $u(\phi_t x)-u(x)=\int_0^t h(\phi_sx)\,ds$. Thus its integral over every periodic orbit is zero. For a transitive <Anosov flow>, the <Livsic theorem> supplies the converse and smooth regularity.