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

Alexander J. Zaslavski

Abstract and Applied Analysis, 2004, vol. 2004, 1-31

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.

Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:106426

DOI: 10.1155/S1085337504310067

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