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Existence and Structure of Extremals for One-Dimensional Nonautonomous Variational Problems

  • A. J. Zaslavski
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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.

Infinite horizons weakly optimal solutions turnpike property minimal average action rotation number 

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Copyright information

© Plenum Publishing Corporation 1998

Authors and Affiliations

  • A. J. Zaslavski
    • 1
  1. 1.Department of MathematicsTechnion-Israel Institute of TechnologyHaifaIsrael

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