Universality of almost periodic orbits in certain composite functions

TL;DR

This paper investigates the behavior of composite functions within elementary algebra, demonstrating the existence of almost periodic orbits without Fourier analysis, and identifying functions that tend asymptotically to these orbits.

Contribution

It introduces a novel algebraic approach to characterize almost periodic orbits in composite functions without relying on Fourier transform techniques.

Findings

Existence of almost periodic orbits in certain composite functions

Construction of composite functions tending asymptotically to almost periodic orbits

Characterization of these orbits within elementary algebraic framework

Abstract

We consider composite functions in the elementary algebraic framework. Without any use of the Fourier transform, we find almost periodic orbits which suitably characterizes certain composite functions. In particular, we provide special composite functions that tend asymptotically to almost periodic orbits.