Chaos and fractals
Subtitle: the mathematics behind the computer graphics
By: Robert L. Devaney and Linda Keen, editors ; [authors] Kathleen T. Alligood ... [et al.].
Contributors: Devaney, Robert L., 1948-; Keen, Linda.; Alligood, Kathleen T.
Series: Proceedings of symposia in applied mathematics,; v. 39.; AMS short course lecture notes; Proceedings of symposia in applied mathematics ;; v. 39.; Proceedings of symposia in applied mathematics.
Publisher: American Mathematical Society
Published: 1989
Place of publication: Providence, RI
Language: eng
Number of pages: 148
Subjects: Computer graphics -- Mathematics; Fractals
Description: The terms chaos and fractals have received widespread attention in recent years. The alluring computer graphics images associated with these terms have heightened interest among scientists in these ideas. This volume contains the introductory survey lectures delivered in the American Mathematical Society Short Course, Chaos and Fractals: The Mathematics Behind the Computer Graphics, on August 6-7, 1988, given in conjunction with the AMS Centennial Meeting in Providence, Rhode Island. In his overview, Robert L. Devaney introduces such key topics as hyperbolicity, the period doubling route to chaos, chaotic dynamics, symbolic dynamics and the horseshoe, and the appearance of fractals as the chaotic set for a dynamical system. Linda Keen and Bodil Branner discuss the Mandelbrot set and Julia sets associated to the complex quadratic family z -> z² + c. Kathleen T. Alligood, James A. Yorke, and Philip J. Holmes discuss some of these topics in higher dimensional settings, including the Smale horseshoe and strange attractors. Jenny Harrison and Michael F. Barnsley give an overview of fractal geometry and its applications. -- from dust jacket.
Notes: Includes bibliographical references and index.
Table of contents: title: Overview : dynamics of simple maps / Robert L. Devaney; title: Nonlinear oscillations and the Smale horseshoe map / Philip J. Holmes; title: Fractal basin boundaries and chaotic attractors / Kathleen T. Alligood and James A. Yorke; title: Julia Sets / Linda Keen; title: The Mandelbrot set / Bodil Branner; title: Introduction to fractals / Jenny Harrison; title: Iterated function systems / Michael F. Barnsley.