Cotangent fiber-dilation flow
= Cotangent fiber-dilation flow
{title2=$D_s(x,p)=(x,e^sp)$}
The vertical <Liouville vector field> on a <cotangent bundle> has complete flow $D_s(x,p)=(x,e^sp)$. Its pullbacks scale both the <Liouville one-form> and the canonical <symplectic form> by $e^s$. As $s\to-\infty$, each orbit tends to its base point on the <zero section>. This contraction proves <rigidity of cotangent Liouville-form preservation>.