Chaos: An Introduction to Dynamical Systems

ISBN-13: 9780387946771 / Angielski / Miękka / 1996 / 603 str.

Kathleen Alligood; Tim Sauer; J. A. Yorke

Opis

Chaos: An Introduction to Dynamical Systems, was developed and class-tested by a distinguished team of authors at two universities through their teaching of courses based on the material. Intended for courses in nonlinear dynamics offered either in Mathematics or Physics, the text requires only calculus, differential equations, and linear algebra as prerequisites. Along with discussions of the major topics, including discrete dynamical systems, chaos, fractals, nonlinear differential equations and bifurcations, the text also includes Lab Visits, short reports that illustrate relevant concepts from the physical, chemical and biological sciences. There are Computer Experiments throughout the text that present opportunities to explore dynamics through computer simulations, designed to be used with any software package. And each chapter ends with a Challenge, which provides students a tour through an advanced topic in the form of an extended exercise.

Recenzje

From the reviews:

"... Written by some prominent contributors to the development of the field ... With regard to both style and content, the authors succeed in introducing junior/senior undergraduate students to the dynamics and analytical techniques associated with nonlinear systems, especially those related to chaos ... There are several aspects of the book that distinguish it from some other recent contributions in this area ... The treatment of discrete systems here maintains a balanced emphasis between one- and two- (or higher-) dimensional problems. This is an important feature since the dynamics for the two cases and methods employed for their analyses may differ significantly. Also, while most other introductory texts concentrate almost exclusively upon discrete mappings, here at least three of the thirteen chapters are devoted to differential equations, including the Poincare-Bendixson theorem. Add to this a discussion of $omega$-limit sets, including periodic and strange attractors, as well as a chapter on fractals, and the result is one of the most comprehensive texts on the topic that has yet appeared." Mathematical Reviews

 

Spis treści

One-Dimensional Maps.- Two-Dimensional Maps.- Chaos.- Fractals.- Chaos in Two-Dimensional Maps.- Chaotic Attractors.- Differential Equations.- Periodic Orbits and Limit Sets.- Chaos in Differential Equations.- Stable Manifolds and Crises.- Bifurcations.- Cascades.- State Reconstruction from Data.