Reconstruction of chaotic orbits under finite resolution

摘要

In this paper, it is shown how information about an orbit of a chaotic dynamical system can be recovered given only measurements with “large” error. Assuming that the imprecision of measurements manifests itself as a finite partition of the phase space, general, necessary, and sufficient conditions under which it is possible to reconstruct orbits are presented. Two reconstructing methods and their pseudocodes are presented and analyzed. The applicability of those methods is tested using a series of computer experiments for various one-dimensional mappings on the unit interval. Potential applications are also discussed.