Discommensuration theory and shadowing in Frenkel–Kontorova models

We prove that if the minimum energy advancing discommensuration of mean spacing p/qp/q for a Frenkel–Kontorova chain is unique up to translations and has phonon gap then all minimum energy states with mean spacing ωω just above p/qp/q are approximated exponentially well in qω−pqω−p by concatenations of advancing p/qp/q discommensurations.