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A First Course In Chaotic Dynamical Systems : Theory And Experiment

Author: Robert L Devaney
Publisher: Boca Raton, FL : CRC Press, 2018.
Edition/Format:   eBook : Document : English : First editionView all editions and formats
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Genre/Form: Electronic books
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Robert L Devaney
ISBN: 9780429503481 0429503482 9780429972034 0429972032
OCLC Number: 1029247160
Description: 1 online resource : text file, PDF
Contents: Cover; Half Title; Title Page; Copyright Page; Preface; Contents; Chapter 1. A Mathematical and Historical Tour; 1.1 Images from Dynamical Systems; 1.2 A Brief History of Dynamics; Chapter 2. Examples of Dynamical Systems; 2.1 An Example from Finance; 2.2 An Example from Ecology; 2.3 Finding Roots and Solving Equations; 2.4 Differential Equations; Chapter 3. Orbits; 3.1 Iteration; 3.2 Orbits; 3.3 Types of Orbits; 3.4 Other Orbits; 3.5 The Doubling Function; 3.6 Experiment: The Computer May Lie; Chapter 4. Graphical Analysis; 4.1 Graphical Analysis; 4.2 Orbit Analysis; 4.3 The Phase Portrait Chapter 5. Fixed and Periodic Points5.1 A Fixed Point Theorem; 5.2 Attraction and Repulsion; 5.3 Calculus of Fixed Points; 5.4 Why Is This True?; 5.5 Periodic Points; 5.6 Experiment: Rates of Convergence; Chapter 6. Bifurcations; 6.1 Dynamics of the Quadratic Map; 6.2 The Saddle-Node Bifurcation; 6.3 The Period-Doubling Bifurcatio n; 6.4 Experiment: The Transition to Chaos; Chapter 7. The Quadratic Family; 7.1 The Case c = -2; 7.2 The Case c < -2; 7.3 The Cantor Middle-Thirds Set; Chapter 8. Transition to Chaos; 8.1 The Orbit Diagram; 8.2 The Period-Doubling Route to Chaos 8.3 Experiment: Windows in the Orbit DiagramChapter 9. Symbolic Dynamics; 9.1 Itineraries; 9.2 The Sequence Space; 9.3 The Shift Map; 9.4 Conjugacy; Chapter 10. Chaos; 10.1 Three Properties of a Chaotic System; 10.2 Other Chaotic Systems; 10.3 Manifestations of Chaos; 10.4 Experiment: Feigenbaum's Constant; Chapter 11. Sarkovskii's Theorem; 11.1 Period 3 Implies Chaos; 11.2 Sarkovskii's Theorem; 11.3 The Period 3 Window; 11.4 Subshifts of Finite Type; Chapter 12. The Role of the Critical Orbit; 12.1 The Schwarzian Derivative; 12.2 The Critical Point and Basins of Attraction Chapter 13. Newton's Method13.1 Basic Properties; 13.2 Convergence and Nonconvergence; Chapter 14. Fractals; 14.1 The Chaos Game; 14.2 The Cantor Set Revisited; 14.3 The Sierpinski Triangle; 14.4 The Koch Snowflake; 14.5 Topological Dimension; 14.6 Fractal Dimension; 14.7 Iterated Function Systems; 14.8 Experiment: Iterated Function Systems; Chapter 15. Complex Functions; 15.1 Complex Arithmetic; 15.2 Complex Square Roots; 15.3 Linear Complex Functions; 15.4 Calculus of Complex Functions; Chapter 16. The Julia Set; 16.1 The Squaring Function; 16.2 The Chaotic Quadratic Function 16.3 Cantor Sets Again16.4 Computing the Filled Julia Set; 16.5 Experiment: Filled Julia Sets and Critical Orbits; 16.6 The Julia Set as a Repellor; Chapter 17. The Mandelbrot Set; 17.1 The Fundamental Dichotomy; 17.2 The Mandelbrot Set; 17.3 Experiment: Periods of Other Bulbs; 17.4 Experiment: Periods of the Decorations; 17.5 Experiment: Find the Julia Set; 17.6 Experiment: Spokes and Antennae; 17.7 Experiment: Similarity of the Mandelbrot and Julia Sets; Chapter 18. Further Projects and Experiments; 18.1 The Tricorn; 18.2 Cubics; 18.3 Exponential Functions; 18.4 Trigonometric Functions
Responsibility: Robert L. Devaney.

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