Encounters with Chaos and Fractals

ISBN-13: 9781584885177 / Angielski / Twarda / 2012 / 387 str.

Denny Gulick; Gulick Gulick

Opis

Now with an extensive introduction to fractal geometry Revised and updated, Encounters with Chaos and Fractals, Second Edition provides an accessible introduction to chaotic dynamics and fractal geometry for readers with a calculus background. It incorporates important mathematical concepts associated with these areas and backs up the definitions and results with motivation, examples, and applications. Laying the groundwork for later chapters, 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 author goes on to introduce famous infinitely complicated fractals. He analyzes them and explains how to obtain computer renditions of them. The book concludes with the famous Julia sets and the Mandelbrot set. With more than enough material for a one-semester course, this book gives readers an appreciation of the beauty and diversity of applications of chaotic dynamics and fractal geometry. It shows how these subjects continue to grow within mathematics and in many other disciplines.

Recenzje

"This text aims to introduce ‘anyone who has a knowledge of calculus’ to ‘chaotic dynamics and fractal geometry at a modest level of sophistication.’ Indeed, the author makes this possible through careful exposition, examples, and exercises …"
—Steve Pederson, Zentralblatt MATH 1253

Spis treści

Periodic Points. One-Dimensional Chaos. Two-Dimensional Chaos. Systems of Differential Equations. Introduction to Fractals. Creating Fractals Sets. Complex Fractals: Julia Sets and the Mandelbrot Set. Computer Programs. Answers to Selected Exercises. References. Index.

O autorze

Denny Gulick is a professor 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.