Reconstruction of chaotic orbits under finite resolution (Q1805268)

The problem of orbit recovering of a chaotic dynamical system under inaccurate state measurements is analyzed. Assuming that only crude qualitative information about the state values, i.e., deciding exclusively whether or not the actual state belongs to some particular set from a finite partition of the phase space, the necessary and sufficient conditions for orbit reconstruction are given. The reconstruction procedures for one-dimensional mappings on the unit interval, together with their pseudocodes and illustrative numerical examples, are provided. Also, efficiency for nonchaotic dynamical systems is evaluated and possible applications are discussed.