Discrete chaos : with applications in science and engineering /: with applications in science and engineering. (2007)

• Record Type: Book
• Further Information: Note: Saber N. Elaydi.
• Other Names: Elaydi, Saber, 1943-
• Contents: PREFACE ; FOREWORD ; The Stability of One-Dimensional Maps ; Introduction; Maps vs. Difference Equations; Maps vs. Differential Equations; Linear Maps/Difference Equations; Fixed (Equilibrium) Points; Graphical Iteration and Stability; Criteria for Stability; Periodic Points and Their Stability; The Period-Doubling Route to Chaos; Applications; Attraction and Bifurcation ; Introduction; Basin of Attraction of Fixed Points; Basin of Attraction of Periodic Orbits; Singer’s Theorem; Bifurcation; Sharkovsky’s Theorem; The Lorenz Map; Period-Doubling in the Real World; Poincaré Section/Map; Appendix; Chaos in One Dimension ; Introduction; Density of the Set of Periodic Points; Transitivity; Sensitive Dependence; Definition of Chaos; Cantor Sets; Symbolic Dynamics; Conjugacy; Other Notions of Chaos; Rössler’s Attractor; Saturn’s Rings; Stability of Two-Dimensional Maps ; Linear Maps vs. Linear Systems; Computing An ; Fundamental Set of Solutions; Second-Order Difference Equations; Phase Space Diagrams; Stability Notions; Stability of Linear Systems; The Trace-Determinant Plane; Liapunov Functions for Nonlinear Maps; Linear Systems Revisited; Stability via Linearization; Applications; Appendix; Bifurcation and Chaos in Two Dimensions ; Center Manifolds; Bifurcation; Hyperbolic Anosov Toral Automorphism; Symbolic Dynamics; The Horseshoe and Hénon Maps; A Case Study: Extinction and Sustainability in Ancient Civilizations; Appendix; Fractals ; Examples of Fractals; L-System; The Dimension of a Fractal; Iterated Function System; Mathematical Foundation of Fractals; The Collage Theorem and Image Compression; The Julia and Mandelbrot Sets ; Introduction; 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 ; Answers to Selected Problems ; Index
• Edition: 2nd ed
• Publisher Details: Place of publication not identified : Chapman and Hall/CRC
• Publication Date: 2007
• Extent: 1 online resource (440 pages), (215 illustrations)
• Subjects: 515.39; Differentiable dynamical systems; Difference equations; Chaotic behavior in systems
• Languages: English
• ISBNs: 9781420011043; 1420011049
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.