ON THE RELATIONSHIP BETWEEN DISCRETE AND CONTINUOUS OBSERVATIONS OF DYNAMICAL SYSTEMS

摘要

In this paper we are concerned with the relationship between the behavior of solutions of continuous dynamical systems that are restricted to a discrete time scale and that of the original solutions. We generalize a classical result of Fink [5, Theorem 9.7] by extending the theory of almost periodic sequence defined on discrete time {t_n}_(n∈ z) which may not have subgroup structure. We also derive a necessary and surfficient condition for the boundedness of solution based on the discrete observations. Some applications to the time-invariant systems and the evolution equations are given.