Discrete chaos

著者

書誌事項

Discrete chaos

Saber N. Elaydi

Chapman & Hall/CRC, c2000

大学図書館所蔵 件 / 全26件

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注記

Includes bibliographical references (p. 333-337) and index

内容説明・目次

内容説明

Over the last 15 years chaos has virtually exploded over the landscape of mathematics and showered its effects on nearly every scientific discipline. However, despite the large number of texts published on the subject, a need has persisted for a book accessible to readers of varying backgrounds that includes discussion of stability theory and emphasizes real-world applications. Discrete Chaos fills that need. With only calculus and linear algebra as prerequisites, this book offers a broad range of topics with a depth not often found in texts written at this level. The author presents a thorough exposition of both stability and chaos theories in both one and two dimensions. He offers a highly readable account of fractals and the mathematics behind them, and demonstrates a number of applications from a variety of fields. This unique treatment of chaos encourages readers to make mathematical discoveries of their own through computer experimentation. The author incorporates the use of Maplea software throughout the book to aid in the solution of problems. All of the programs used in the book can be easily downloaded from the Internet. You'll find even the most difficult material in an elementary framework, easily accessible regardless of your background and specialization. With a multitude of exercises to further enhance the learning experience, Discrete Chaos offers the perfect vehicle for beginning the journey into the rich world of chaos.

目次

The Stability of One-Dimensional Maps Maps Versus Difference Equations Maps Versus Differential Equations Linear Maps/Difference Equations Fixed Points Graphical Iteration and Stability Criteria for Stability Periodic Points and Their Stability The Period-Doubling Route to Chaos Applications Sharkovsky's Theorem and Bifurcation The Mystery of Period 3 Converse of Sharkovsky's Theorem Basin of Attraction The Schwarzian Derivative Bifurcation The Lorenz Map Chaos in One Dimension Introduction Metric Spaces Transitivity Sensitive Dependence and Liapunov Exponents Definition and Chaos Symbolic Dynamics Conjugacy Stability of Two-Dimensional Maps Linear Maps Versus Linear Systems Computing An Phase Space Liapunov Functions for Nonlinear Maps Linear Systems Revisited Stability via Linearization Applications Chaos in Two Dimensions Hyperbolic Anosov Toral Automorphism Symbolic Dynamics The Horseshoe and Henon Maps Center Manifolds Bifurcation Fractals Examples of Fractals The Dimension of Fractal Iterated Function System Mathematical Foundation of Fractals The Collage Theorem and Image Compression The Julia and Mandelbrot Sets Mapping by Functions on the Complex Domain The Riemann Sphere The Julia Set Topological Properties of the Julia Set Newton's Method in the Complex Plane The Mandelbrot Set Bibliography

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