Abstract and Applied Analysis
Volume 2004 (2004), Issue 8, Pages 691-721

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

Alexander J. Zaslavski

Department of Mathematics, Technion – Israel Institute of Technology, Haifa 32000, Israel

Received 18 November 2002

Copyright © 2004 Alexander J. Zaslavski. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.