Fixed points of the Bellman operator semi-groups and invariant manifolds of subdifferential Hamiltonian equations

Stationar dynamic optimization problems are considered in Lagrangean form on a stretch of variable length. Obtaining extremal curves independent of the optimization horizon is discussed. A terminal term is proved to exist whose addition to the integral functional which specifies the optimization criterion results in a problem whose extremal curves are Markov. The key role in the design is played by the Bellman operator semi-group, a notion introduced in the paper. The relationship is studied of stationary orbits of the semi-group with invariant manifolds of Hamiltonian systems. The results are applied to analysis of one class of economic dynamics models.