Basic feature quantities for analysis of periodic orbits in digital return maps
Tada Naoki, Toshimichi Saito · Nonlinear Theory and Its Applications IEICE · 2017
This paper studies digital return maps defined on a set of points.Depending on parameters and initial states, the maps can generate a variety of periodic orbits.In order to analyze the periodic orbits, we present two feature quantities.The first and second quantities can characterize the plentifulness and a variety of periodic orbits, respectively.Constructing a feature plane of the two quantities, the dynamics of the map can be visualized.Using the feature quantities and feature plane, we investigate various periodic orbits in digital return maps derived from a basic class of cellular automata.