Title: Chaos : an introduction to dynamical systems /
Authors: Alligood, Kathleen T.; Sauer, Tim.; Yorke, James A.
Publisher: Springer,
Year: 1997
Subjects: Differentiable dynamical systems.; Chaotic behavior in systems; Mathematics; Global analysis (Mathematics).; Physics; Engineering
Abstract: 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.
Contents: Preface -- One-Dimensional Maps -- Two-dimensional Maps -- Chaos -- Fractals -- Chaos in Two-Dimensional Maps -- Chaotic Attractors -- Differential Equations -- Periodic Orbits and Limited Sets -- Chaos in Differential Equations -- Stable Manifolds and Crises -- Bifurcations -- Cascades -- State Reconstruction of Data -- Appendices A & B -- Answers and Hints to Selected Exercises -- Bibliography -- Index.