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Asymptotes of optimal trajectories

  • V. L. Makarov
  • A. M. Rubinov

Abstract

In this section we only consider Neumann-Gale models Z that possess equilibrium states. We assume throughout, except for the last subsection, that the model Z is regular (i.e., Pr1Z = ℝ+ n ). In this case, the set of all trajectories of the model Z coincides with the trajectory bundle of the model 𝔐z (Section 3.3):
$$ {{\mathfrak{M}}_{z}} = \left\{ {\left\{ {0,1,2,...} \right\},{{{\left( {{{X}_{t}}} \right)}}^{\infty }}_{{{\text{t }} = 0}},{{{\left( {{{K}_{t}}} \right)}}^{\infty }}_{{{\text{t }} = 0}},{{{\left( {{{a}_{{\tau ,t}}}} \right)}}_{{0{\text{ t }} < \infty }}}} \right\} $$
where X t = ℝ n , K t = ℝ+ n for t = 0, 1,..., and a τ,t = a τ-t for 0 ≤ t < τ < ∞, (here a is the generating map of model Z). In the last subsection we consider arbitrary Neumann-Gale models.

Keywords

Natural Number Convex Cone Optimal Trajectory Polyhedral Cone Characteristic Compactum 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York, Inc. 1977

Authors and Affiliations

  • V. L. Makarov
    • 1
  • A. M. Rubinov
    • 1
  1. 1.Siberian Branch of the Academy of SciencesRussia

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