A Energy hypersurface in a phase space (statistical physics)

daniel444
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what is the reason for that the energy hypersurfaces in a phase space, which belong to systems with constant energy are closed? ( see picture )
237D2118-2CA1-4598-8FEF-7CF73AA8F22C.jpeg
 
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If not closed, there would be no border between higher energy region and lower energy region. No energy contour. No grad. No force.
 

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