In discrete schemes, weak KAM solutions may be interpreted as approximations
of correctors for some Hamilton-Jacobi equations in the periodic setting. It is
known that correctors may not exist in the almost periodic setting. We show the
existence of discrete weak KAM solutions for non-degenerate and weakly twist
interactions in general. Furthermore, assuming equivariance with respect to a
linearly repetitive quasi-periodic set, we completely classify all possible
types of weak KAM solutions.Comment: 44 pages, 1 figur