We introduce the concepts of perpetual points and periodic perpetual loci in discrete-time systems (maps). The occurrence and analysis of these points/loci are shown and basic examples are considered. We discuss the potential usage and properties of the introduced concepts. The comparison of perpetual points and loci in discrete-time and continuous-time systems is presented. The discussed methods can be widely applied in other dynamical systems.
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Dudkowski et al. (2016) studied this question.
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