  But in the last section of the paper he suddenly shifts course. He now focuses on a general Hamiltonian system, i.e., a system of N material points with an arbitrary interaction potential. The state of this system may be represented as a phase point \(x = (\vec{p}_1,\ldots,\vec{p}_N,\vec{q}_1,\ldots,\vec{q}_N)\) in the mechanical phase space \(\Gamma\). By the Hamiltonian equations of motion, this point evolves in time, and thus describes a trajectory \(x_t\). This trajectory is constrained to lie on a given energy hypersurface \(H(x) = E\), where \(H(x)\) denotes the Hamiltonian function.