Existence and numerical approximation of periodic motions of an infinite lattice of particles. (English) Zbl 0838.34046

The lattice is autonomous. Its particles interact with their nearest neighbours by a force belonging to a certain class characterized by the properties of the potential. Purely attractive forces are considered. Assumptions are given which admit a nonzero periodic non constant solution with finite energy. First, a finite system is considered, then an appropriate imbedding of this case in the infinite system is given and the limit process is taken. The application of a known algorithm is shown for finite lattices in the case of repulsive-attractive forces; investigating the infinite lattices a process of approximation in the proof is based on these results. Some numerical experiments for finite lattices are shown.


34C25 Periodic solutions to ordinary differential equations
70F99 Dynamics of a system of particles, including celestial mechanics
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