Abstract
We study the existence and structure of extremals for one-dimensional variational problems on a torus and the properties of the minimal average action as a function of the rotation number. We show that, for a generic integrand f, the minimum of the minimal average action is attained at a rational point mn −1 where n≥1 and m are integers; also, for each initial value, there exists an (f)-weakly optimal solution over an infinite horizon.
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Zaslavski, A.J. Existence and Structure of Extremals for One-Dimensional Nonautonomous Variational Problems. Journal of Optimization Theory and Applications 97, 731–757 (1998). https://doi.org/10.1023/A:1022602512064
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DOI: https://doi.org/10.1023/A:1022602512064