Monotone gradient dynamics and the location of stationary (p,q)-configurations

By exploiting the monotone property of the gradient dynamics of the Frenkel–Kontorova model, we are able to locate the ordered and unordered stationary states in the space of (p, q)-configurations, as well as forbidden regions for such states. Moreover, we will show that some generalized Frenkel–Kontorova models (which are associated with multiharmonic standard maps) can have ordered (p, q)-configurations that are neither action minimizing nor mini-maximizing, and we give their location with respect to the set of (p, q)-minimizers and mini-maximizers. (paper)