Perpetual points and periodic perpetual loci in maps

Abstract

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 introduced concepts. The comparison of perpetual points and loci in discrete--time and continuous--time systems is presented. Discussed methods can be widely applied in other dynamical systems.

References in corpus (2)

• Homoclinic orbits, and self-excited and hidden attractors in a Lorenz-like system describing convective fluid motion
• Existence of perpetual points in nonlinear dynamical systems and its applications

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