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

Emilia Petrisor
2014 Journal of Physics A: Mathematical and Theoretical  
Exploiting the monotone property of the gradient dynamics of the Frenkel-Kontorova model, we locate in the space of (p,q)-configurations the ordered and unordered stationary states, as well as forbidden regions for such states. Moreover we show that some generalized Frenkel--Kontorova models (associated to multiharmonic standard maps) can have ordered (p,q)--configurations that are neither action minimizing nor minimaximizing, and give their location with respect to the set of (p,q)--minimizers and minimaximizers.
doi:10.1088/1751-8113/47/4/045102 fatcat:lfggqvmgqjdsdiss2wavl45ud4