Limited Computational Ability and Approximation of Dynamical Systems

This paper is devoted to the theoretical aspects of approximating dynamical systems and to some possible applications in economics. The approach presented here is based on the notion of the shadowing property of a dynamical system and on the use of pseudotrajectories to approximate true orbits. In particular, specific results in the case of attractors and the notion of generalized shadowing are reviewed. The final sections deal with economic applications and suggest a range of situations in which the type of bounded computational ability depicted here might be relevant.