  In this paper the turnpike property is established for a non-convex optimal
control problem in discrete time. The functional is defined by the notion of
the ideal convergence and can be considered as an analogue of the terminal
functional defined over infinite time horizon. The turnpike property states
that every optimal solution converges to some unique optimal stationary point
in the sense of ideal convergence if the ideal is invariant under translations.
This kind of convergence generalizes, for example, statistical convergence and
convergence with respect to logarithmic density zero sets.
