Chaos and fractals an elementary introduction
Chaos and fractals: an elementary introduction
Gespeichert in:
Bibliographische Detailangaben
1. Verfasser: Feldman, David P. (VerfasserIn)
Format: Elektronisch E-Book
Sprache:English
Veröffentlicht: Oxford Oxford University Press 2012
Schlagworte:
MATHEMATICS / Topology
Chaotic behavior in systems
Fractals
Fraktal
Chaotisches System
Online-Zugang:FAW01
FAW02
Volltext
Beschreibung:Includes bibliographical references and index
For students with a background in elementary algebra, this text provides a vivid introduction to the key phenomena and ideas of chaos and fractals, including the butterfly effect, strange attractors, fractal dimensions, Julia sets and the Mandelbrot set, power laws, and cellular automata
Cover; Contents; I: Introducing Discrete Dynamical Systems; 0 Opening Remarks; 0.1 Chaos; 0.2 Fractals; 0.3 The Character of Chaos and Fractals; 1 Functions; 1.1 Functions as Actions; 1.2 Functions as a Formula; 1.3 Functions are Deterministic; 1.4 Functions as Graphs; 1.5 Functions as Maps; Exercises; 2 Iterating Functions; 2.1 The Idea of Iteration; 2.2 Some Vocabulary and Notation; 2.3 Iterated Function Notation; 2.4 Algebraic Expressions for Iterated Functions; 2.5 Why Iteration?; Exercises; 3 Qualitative Dynamics: The Fate of the Orbit; 3.1 Dynamical Systems
3.2 Dynamics of the Squaring Function3.3 The Phase Line; 3.4 Fixed Points via Algebra; 3.5 Fixed Points Graphically; 3.6 Types of Fixed Points; Exercises; 4 Time Series Plots; 4.1 Examples of Time Series Plots; Exercises; 5 Graphical Iteration; 5.1 An Initial Example; 5.2 The Method of Graphical Iteration; 5.3 Further Examples; Exercises; 6 Iterating Linear Functions; 6.1 A Series of Examples; 6.2 Slopes of +1 or -1; Exercises; 7 Population Models; 7.1 Exponential Growth; 7.2 Modifying the Exponential Growth Model; 7.3 The Logistic Equation; 7.4 A Note on the Importance of Stability
7.5 Other r ValuesExercises; 8 Newton, Laplace, and Determinism; 8.1 Newton and Universal Mechanics; 8.2 The Enlightenment and Optimism; 8.3 Causality and Laplace's Demon; 8.4 Science Today; 8.5 A Look Ahead; II: Chaos; 9 Chaos and the Logistic Equation; 9.1 Periodic Behavior; 9.2 Aperiodic Behavior; 9.3 Chaos Defined; 9.4 Implications of Aperiodic Behavior; Exercises; 10 The Butterfly Effect; 10.1 Stable Periodic Behavior; 10.2 Sensitive Dependence on Initial Conditions; 10.3 SDIC Defined; 10.4 Lyapunov Exponents; 10.5 Stretching and Folding: Ingredients for Chaos
10.6 Chaotic Numerics: The Shadowing LemmaExercises; 11 The Bifurcation Diagram; 11.1 A Collection of Final-State Diagrams; 11.2 Periodic Windows; 11.3 Bifurcation Diagram Summary; Exercises; 12 Universality; 12.1 Bifurcation Diagrams for Other Functions; 12.2 Universality of Period Doubling; 12.3 Physical Consequences of Universality; 12.4 Renormalization and Universality; 12.5 How are Higher-Dimensional Phenomena Universal?; Exercises; 13 Statistical Stability of Chaos; 13.1 Histograms of Periodic Orbits; 13.2 Histograms of Chaotic Orbits; 13.3 Ergodicity; 13.4 Predictable Unpredictability
Exercises14 Determinism, Randomness, and Nonlinearity; 14.1 Symbolic Dynamics; 14.2 Chaotic Systems as Sources of Randomness; 14.3 Randomness?; 14.4 Linearity, Nonlinearity, and Reductionism; 14.5 Summary and a Look Ahead; Exercises; III: Fractals; 15 Introducing Fractals; 15.1 Shapes; 15.2 Self-Similarity; 15.3 Typical Size?; 15.4 Mathematical vs. Real Fractals; Exercises; 16 Dimensions; 16.1 How Many Little Things Fit inside a Big Thing?; 16.2 The Dimension of the Snowflake; 16.3 What does D {u2248} 1.46497 Mean?; 16.4 The Dimension of the Cantor Set; 16.5 The Dimension of the Sierpiński Triangle
Beschreibung:1 Online-Ressource (xxi, 408 pages)
ISBN:0191637521
0199566437
0199566445
128364388X
9780191637520
9780199566433
9780199566440
9781283643887

Es ist kein Print-Exemplar vorhanden.

Fernleihe Bestellen Achtung: Nicht im THWS-Bestand! Volltext öffnen

Ähnliche Einträge