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Structural stability of classical lattices in one dimension. (English) Zbl 0557.58017
From the authors’ abstract: ”We prove the structural stability of the property for a two-body potential to give rise to a one-dimensional lattice in some suitable sense: it is required that a sequence of stable equilibria of n particles exists, such that in the limit \(n\to \infty\), the average spacings converge, the dispersions remain bounded and some uniformity of the stability is assumed. Then all neighboring potentials satisfy similar conditions, thus providing open sets of interactions in the Whitney topology, which give rise to lattices in the above sense. Moreover, assuming further realistic conditions on the potential, we prove the structurally stable lattice to be and to remain the ground state.”
Reviewer: M.A.Teixeira

MSC:
37C75 Stability theory for smooth dynamical systems
34D30 Structural stability and analogous concepts of solutions to ordinary differential equations
82D25 Statistical mechanics of crystals
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