Perpetual points and periodic perpetual loci in maps
Dawid Dudkowski, Awadhesh Prasad, Tomasz Kapitaniak
TL;DR
This paper introduces the concepts of perpetual points and periodic perpetual loci in discrete-time systems, analyzing their properties, occurrence, and potential applications, and comparing them with continuous-time systems.
Contribution
It presents new definitions and analysis methods for perpetual points and loci in maps, expanding understanding of their role in dynamical systems.
Findings
Perpetual points and loci can be identified in various maps.
Properties of perpetual points differ between discrete and continuous systems.
Methods for analyzing these points are broadly applicable.
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.
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