Liouville's theorem in the context of Hamiltonian mechanics is a fundamental result concerning the conservation of phase space volume in a dynamical system. The theorem states that the flow of a Hamiltonian system preserves the volume in phase space. More formally, consider a Hamiltonian system described by \( (q, p) \), where \( q \) represents the generalized coordinates and \( p \) represents the generalized momenta.
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