Encounters with Chaos and Fractals

Encounters with Chaos and Fractals, Third Edition provides an accessible introduction to chaotic dynamics and fractal geometry. It incorporates important mathematical concepts and backs up the definitions and results with motivation, examples, and applications.

Encounters with Chaos and Fractals, Third Edition provides an accessible introduction to chaotic dynamics and fractal geometry. It incorporates important mathematical concepts and backs up the definitions and results with motivation, examples, and applications.

The third edition updates this classic book for a modern audience. New applications on contemporary topics, like data science and mathematical modeling, appear throughout. Coding activities are transitioned to open-source programming languages, including Python.

The text begins with examples of mathematical behavior exhibited by chaotic systems, first in one dimension and then in two and three dimensions. Focusing on fractal geometry, the authors introduce famous, infinitely complicated fractals. How to obtain computer renditions of them is explained. The book concludes with Julia sets and the Mandelbrot set.

The Third Edition includes:

• More coding activities incorporated in each section with expanded code to include pseudo-code, with specific examples in MATLAB® (or its open-source cousin Octave) and Python
• Additional exercises-many updated-from previous editions
• Proof-writing exercises for a more theoretical course
• Revised sections to include historical context

• Short sections added to explain applied problems in developing mathematics This edition reveals how these ideas are continuing to be applied in the 21st century, while connecting to the long and winding history of dynamical systems. The primary focus is the beauty and diversity of these ideas. Offering more than enough material for a one-semester course, the authors show how these subjects continue to grow within mathematics and in many other disciplines.

  Autorentext

  Denny Gulick is Professor Emeritus in the Department of Mathematics at the University of Maryland. His research interests include operator theory and fractal geometry. He earned a PhD from Yale University.

Jeff Ford is a Visiting Assistant Professor of Mathematics at Gustavus Adolphus College. He earned his Bachelor's degree from Gustavus Adolphus College, his Master's degree in mathematics from Minnesota State University-Mankato, and his Ph.D. in mathematics from Auburn University, studying under Dr. Krystyna Kuperberg. Jeff is interested in the existence of volume-preserving dynamical systems with unique properties. Jeff uses and assesses a variety of active learning techniques in his class including inquiry-based learning and team-based learning. His scholarship in this area centers on understanding how active learning techniques improve confidence and reduce anxiety in undergraduate students.

Inhalt

Chapter 1. Periodic Points. Chapter 2. One-Dimensional Chaos. Chapter 3. Two-Dimensional Chaos. Chapter 4. Systems of Differential Equations. Chapter 5. Introduction to Fractals. Chapter 6. Creating Fractal Sets. Chapter 7. Complex Fractals: Julia Sets and The Mandelbrot.