Abstract and Applied Analysis
Volume 2004 (2004), Issue 8, Pages 691-721
doi:10.1155/S1085337504310067

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

Abstract

We study (h)-minimal configurations in Aubry-Mather theory, where h belongs 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 element h of this set and each rational number α, the following properties hold: (i) there exist three different (h)-minimal configurations with rotation number α; (ii) any (h)-minimal configuration with rotation number α is a translation of one of these configurations.