Perpetual points and periodic perpetual loci in maps

摘要

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. Published by AIP Publishing.