Dynamics of Entire Functions

The Fractal Sets of Julia and Mandelbrot

Cándido Piñeiro

• Publisher: De Gruyter
• Year: 2025
• eBook ISBN: 9783111690292
• Edition: 0
• Topic: Mathematics
• Subtopic: Computer Science General
• Index: Mathematics

There are very few systematic books on the dynamics of entire functions. Unfortunately, reading these books is often difficult for non-specialists since their proofs are not clearly written, and readers struggle to understand the arguments fully. This book is a comprehensive introduction to the iteration theory of entire complex functions. It is intended to introduce the reader to the key topics in the field and to form a basis for further study. In general, the proofs are more detailed; therefore, the book will also help non-specialist mathematicians become acquainted with complex dynamics. In no sense is this manuscript a complete account of the subject. Nevertheless, the book may also be helpful to young researchers in this field before they tackle more specific works. The book deals with three possible aspects: theory, practice, and computer graphics. In Appendix C, we explained the necessary rudiments of MATLAB RGB images to create computer graphics of different sets considered in the book, such as the sets of Julia and Mandelbrot. In this Appendix, a gallery is also included where beautiful and spectacular images are shown. The author has obtained all these images using MATLAB, most of which are revealed here for the first time.

Table of contents

• Title Page
• Copyright
• Contents
• Preface
• 1 Introduction
• 2 Normal families
• 3 Value distribution theory
• 4 Periodic points
• 5 Local conjugacy
• 6 The Fatou and Julia sets
• 7 Fatou components
• 8 Singular values
• 9 The exponential family
• 10 The parameter plane
• 11 Convergence and dynamics
• Subject Index