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

Alexander J. Zaslavski

Abstract and Applied Analysis, 2004, vol. 2004, issue 8, 691-721

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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https://doi.org/10.1155/S1085337504310067

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2004:y:2004:i:8:p:691-721

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