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Turnpike property for extremals of variational problems with vector-valued functions

1999
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Transactions of the American Mathematical Society
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In this paper we study the structure of extremals ν : [0, T ] → R n of variational problems with large enough T , fixed end points and an integrand f from a complete metric space of functions. We will establish the turnpike property for a generic integrand f . Namely, we will show that for a generic integrand f , any small ε > 0 and an extremal ν : [0, T ] → R n of the variational problem with large enough T , fixed end points and the integrand f , for each τ ∈ [L 1 , T − L 1 ] the set {ν(t): t

doi:10.1090/s0002-9947-99-02132-7
fatcat:shtilqz4jjf6bgnn7uaj75hqxe