Limited Computational Ability and Approximation of Dynamical Systems

This paper addresses problems due to approximation of dynamical systems. 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 evidence described may be relevant for a wide range of economic models, whenever agents that have limited computational ability, such as agents relying on digital computers, are concerned. The final section presents two sample applications to economic models.