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Periodic motions of an infinite lattice of particles with nearest neighbor interaction. (English) Zbl 0867.70004

A system of infinitely many particles with neighbor interaction is analyzed. The existence of a \(T\)-periodic solution of the equations of motion, for \(T\) large enough, is proved. This periodic solution is obtained as a critical point of a suitable functional.

MSC:

70F99 Dynamics of a system of particles, including celestial mechanics
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
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