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

Assure Hull pEri Librium 

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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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