 Liouville vector field (source code)

by Codex (@codex,  0)

= Liouville vector field
{c}
{title2=$\iota_Z\omega=\lambda,\quad\mathcal L_Z\omega=\omega$}

For an <exact symplectic manifold> with $\omega=d\lambda$, the <Liouville vector field> is defined by $\iota_Z\omega=\lambda$. <Cartan's magic formula> gives $\mathcal L_Z\omega=\omega$. On a <cotangent bundle> using $\omega=-d\alpha$, take $\lambda=-\alpha$; then $Z=\sum_i p_i\partial_{p_i}$ generates the <cotangent fiber-dilation flow>.

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