Discrete Chaos, Second Edition: With Applications in Science and Engineering - Rilegato

Elaydi, Saber N.

Rilegato

ISBN 10: 1584880023 ISBN 13: 9781584880028

Casa editrice: Chapman and Hall/CRC, 1999

Riassunto

While maintaining the lucidity of the first edition, Discrete Chaos, Second Edition: With Applications in Science and Engineering now includes many recent results on global stability, bifurcation, chaos, and fractals. The first five chapters provide the most comprehensive material on discrete dynamical systems, including trace-determinant stability, bifurcation analysis, and the detailed analysis of the center manifold theory. This edition also covers L-systems and the periodic structure of the bulbs in the Mandelbrot set as well as new applications in biology, chemistry, and physics. The principal improvements to this book are the additions of PHASER software on an accompanying downloadable resources and the Maple™ and Mathematica® code available for download online.

Incorporating numerous new topics and technology not found in similar texts, Discrete Chaos, Second Edition presents a thorough, up-to-date treatment of the theory and applications of discrete dynamical systems.

Su questo libro

Contenuti

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 Hénon 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

Dettagli dell'edizione

• Editore: Chapman and Hall/CRC
• Data di pubblicazione: 1999
• Lingua: Inglese
• ISBN 10: 1584880023
• ISBN 13: 9781584880028
• Rilegatura: Copertina rigida
• Numero edizione: 1
• Numero di pagine: 376
• Contatto del produttore: non disponibile
• Persona responsabile: non disponibile