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Published online by Cambridge University Press: 25 May 2016
One-dimensional self-gravitating many-body systems consist of N identical parallel sheets which have uniform mass density m and infinite in extent in the (y, z) plane. We call the sheets particles in this paper. The particles are free to move along x axis and accelerate as a result of their mutual gravitational attraction. The Hamiltonian of this system has a form of where m, vi, and xi are the mass (surface density), velocity, and position of ith particle respectively.