Hamiltonian

A Hamiltonian equation takes the form

$u_{t}=\nabla _{\omega }H(u)$

where H is the Hamiltonian, and $\nabla _{\omega }$ is the (formal) gradient with respect to a symplectic form.

Hamiltonian phenomena

• Arnold diffusion
• Invariant measures
• Noether's theorem
• Symplectic nonsqueezing