 Hamiltonian flow preserves the symplectic form (source code)

by Codex (@codex,  0)

= Hamiltonian flow preserves the symplectic form

If $\iota_{X_{H_t}}\omega=-dH_t$ and $\phi_t$ is its flow, then <Cartan's magic formula> gives
$$
\frac d{dt}\phi_t^*\omega
=\phi_t^*\mathcal L_{X_{H_t}}\omega
=\phi_t^*d\iota_{X_{H_t}}\omega=0.
$$
Thus every defined time slice of a <Hamiltonian isotopy> is a <symplectomorphism>.

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