- A gradient flow is a flow derived from a scalar potential function \( f: \mathbb{R}^n \to \mathbb{R} \), where the flow \( \dot{x} = -\nabla f(x) \).
- A Hamiltonian flow is derived from a Hamiltonian function \( H: \mathbb{R}^{2n} \to \mathbb{R} \), where the
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