Generic uniqueness of minimal configurations with rational rotation numbers in Aubry-Mather theory

摘要

We study(h)-minimal configurations in Aubry-Mather theory, wherehbelongs to a complete metric space of functions. Such minimal configurations have definite rotation number. We establish the existence of a set of functions, which is a countable intersection of open everywhere dense subsets of the space and such that for each elementhof this set and each rational numberα, the following properties hold: (i) there exist three different(h)-minimal configurations with rotation numberα; (ii) any(h)-minimal configuration with rotation numberαis a translation of one of these configurations.