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We study the turnpike property for the nonconvex optimal controlproblems described by the differential inclusion x˙∈a(x). We study the infinite horizon problem of maximizing the functional ∫0Tu(x(t))dt as T grows to infinity. The turnpike theorem is proved for the case when a turnpike set consists of several optimal stationary points

A turnpike theorem for continuous-time control systems when the optimal stationary point is not unique