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dyn

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I am working through some notes on the above 2 theorems.

Liouville's Theorem states that the volume of a region of phase space is constant along Hamiltonian flows so i assume this means dV/dt = 0

In the notes on the Poincare Recurrence Theorem it states that if V(t) is the volume of phase space swept out in time t then since volume is preserved dV/dt = C where C≥ 0 is constant. Surely by Liouville's Theorem C should be zero ?

Thanks