Filled Julia and Mandelbrot Sets for Dynamics over the Normed Real Nonassociative Algebras

TL;DR

This paper extends the concepts of filled Julia and Mandelbrot sets to dynamical systems over normed real nonassociative algebras, exploring their properties and applications beyond classical complex dynamics.

Contribution

It introduces a new framework for dynamical systems over nonassociative algebras and generalizes classical fractal sets to this broader context.

Findings

Generalized filled Julia and Mandelbrot sets for nonassociative algebras

Analyzed orbit structures and topological properties

Provided applications of the generalized sets

Abstract

In this paper we introduce the notion of dynamical systems over the class of the normed real nonassociative algebras not necessarily finite-dimensional, generalize the classical filled Julia and Mandelbrot sets over the complex numbers, investigate their orbits and make a topological analysis. Applications of the obtained results are made.