## 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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### References:

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