An Introduction To Chaotic Dynamical Systems
2nd Edition
Published on 7. February 2003
Book
Paperback/Softback
360 pages
978-0-8133-4085-2 (ISBN)
Description
The study of nonlinear dynamical systems has exploded in the past 25 years, and Robert L. Devaney has made these advanced research developments accessible to undergraduate and graduate mathematics students as well as researchers in other disciplines with the introduction of this widely praised book. In this second edition of his best-selling text, Devaney includes new material on the orbit diagram fro maps of the interval and the Mandelbrot set, as well as striking color photos illustrating both Julia and Mandelbrot sets. This book assumes no prior acquaintance with advanced mathematical topics such as measure theory, topology, and differential geometry. Assuming only a knowledge of calculus, Devaney introduces many of the basic concepts of modern dynamical systems theory and leads the reader to the point of current research in several areas.
More details
Edition
2nd edition
Language
English
Place of publication
Oxford
United States
Publishing group
Taylor & Francis Inc
Target group
College/higher education
Product notice
Paperback (trade)
Dimensions
Height: 229 mm
Width: 152 mm
Thickness: 20 mm
Weight
522 gr
ISBN-13
978-0-8133-4085-2 (9780813340852)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
New editions
Robert L. Devaney
An Introduction To Chaotic Dynamical Systems
Book
08/2024
3rd Edition
Chapman & Hall/CRC
€119.00
Shipment within 15-20 days
Additional editions
Robert Devaney
An Introduction To Chaotic Dynamical Systems
Book
06/2019
2nd Edition
CRC Press
€179.51
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Person
Professor Robert L. Devaney received his A.B. from Holy Cross College and his Ph.D. from the University of California at Berkeley in 1973. He taught at Northwestern University, Tufts University, and the University of Maryland before coming to Boston University in 1980. He served there as chairman of the Department of Mathematics from 1983 to 1986. His main area of research is dynamical systems, including Hamiltonian systems, complex analytic dynamics, and computer experiments in dynamics. He is the author of An Introduction to Chaotic Dynamical Systems, and Chaos, Fractals, and Dynamics: Computer Experiments in Modern Mathematics, which aims to explain the beauty of chaotic dynamics to high school students and teachers.
Content
Part One: One-Dimensional Dynamics * Examples of Dynamical Systems * Preliminaries from Calculus * Elementary Definitions * Hyperbolicity * An example: the quadratic family * An Example: the Quadratic Family * Symbolic Dynamics * Topological Conjugacy * Chaos * Structural Stability * Sarlovskiis Theorem * The Schwarzian Derivative * Bifurcation Theory * Another View of Period Three * Maps of the Circle * Morse-Smale Diffeomorphisms * Homoclinic Points and Bifurcations * The Period-Doubling Route to Chaos * The Kneeding Theory * Geneaology of Periodic Units Part Two: Higher Dimensional Dynamics * Preliminaries from Linear Algebra and Advanced Calculus * The Dynamics of Linear Maps: Two and Three Dimensions * The Horseshoe Map * Hyperbolic Toral Automorphisms * Hyperbolicm Toral Automorphisms * Attractors * The Stable and Unstable Manifold Theorem * Global Results and Hyperbolic Sets * The Hopf Bifurcation * The Hnon Map Part Three: Complex Analytic Dynamics * Preliminaries from Complex Analysis * Quadratic Maps Revisited * Normal Families and Exceptional Points * Periodic Points * The Julia Set * The Geometry of Julia Sets * Neutral Periodic Points * The Mandelbrot Set * An Example: the Exponential Function