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The anti-continuum limit of a monotone variational recurrence relationconsists of a lattice of uncoupled particles in a periodic background. Thislimit supports many trivial equilibrium states that persist as solutions of themodel with small coupling. We investigate when a persisting solution generatesa so-called lamination and prove that near the anti-continuum limit thecollection of laminations of solutions is homeomorphic to the (N-1)-dimensionalsimplex, with N the number of distinct local minima of the backgroundpotential. This generalizes a result by Baesens and MacKay on twist maps nearan anti-integrable limit.

The laminations of a crystal near an anti-continuum limit