Derivation of Higher Dimensional Periodic Recurrence Equations by Nested Structure of Complex Numbers

TL;DR

This paper presents a method to derive higher-dimensional periodic recurrence equations using the nested structure of complex numbers, expanding the mathematical tools for analyzing complex dynamical systems.

Contribution

It introduces a novel procedure for deriving higher-dimensional PREs based on complex number nesting, which was not previously established.

Findings

Provides a systematic derivation method for higher-dimensional PREs.

Demonstrates the applicability of complex number nesting in dynamical systems.

Enables new analysis techniques for complex periodic behaviors.

Abstract

In this paper, we give a procedure for derivation of higher dimensional periodic recurrence equations(PREs) by nested structure of complex numbers.