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Discrete and Continuous Observations on the Relationship between Discrete and Continuous Observations of Dynamical Systems $43.00
Authors:  Bui Xuan Dieu, Do Duc Thuan, Ha Binh Minh and Nguyen Van Minh
Abstract:
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 {tn}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. 


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Discrete and Continuous Observations on the Relationship between Discrete and Continuous Observations of Dynamical Systems