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catalog contributor b3933492.
catalog created "c1992.".
catalog date "1992".
catalog date "c1992.".
catalog dateCopyrighted "c1992.".
catalog description "Ch. 1. A Mathematical and Historical Tour. 1.1. Images from Dynamical Systems. 1.2. A Brief History of Dynamics -- Ch. 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 -- Ch. 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 -- Ch. 4. Graphical Analysis. 4.1. Graphical Analysis. 4.2. Orbit Analysis. 4.3. The Phase Portrait -- Ch. 5. Fixed and Periodic Points. 5.1. 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 -- Ch. 6. Bifurcations. 6.1. Dynamics of the Quadratic Map. 6.2. The Saddle-Node Bifurcation. 6.3. The Period-Doubling Bifurcation. 6.4. Experiment: The Transition to Chaos -- ".
catalog description "Ch. 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 -- Ch. 15. Complex Functions. 15.1. Complex Arithmetic. 15.2. Complex Square Roots. 15.3. Linear Complex Functions. 15.4. Calculus of Complex Functions -- Ch. 16. The Julia Set. 16.1. The Squaring Function. 16.2. The Chaotic Quadratic Function. 16.3. Cantor Sets Again. 16.4. Computing the Filled Julia Set. 16.5. Experiment: Filled Julia Sets and Critical Orbits. 16.6. The Julia Set as a Repellor -- Ch. 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 -- ".
catalog description "Ch. 18. Further Projects and Experiments. 18.1. The Tricorn. 18.2. Cubics. 18.3. Exponential Functions. 18.4. Trigonometric Functions. 18.5. Complex Newton's Method -- Appendix A. Mathematical Preliminaries -- Appendix B. Algorithms -- Appendix C. References.".
catalog description "Ch. 7. The Quadratic Family. 7.1. The Case c = -2. 7.2. The Case c [actual symbol not reproducible] -2. 7.3. The Cantor Middle-Thirds Set -- Ch. 8. Transition to Chaos. 8.1. The Orbit Diagram. 8.2. The Period-Doubling Route to Chaos. 8.3. Experiment: Windows in the Orbit Diagram -- Ch. 9. Symbolic Dynamics. 9.1. Itineraries. 9.2. The Sequence Space. 9.3. The Shift Map. 9.4. Conjugacy -- Ch. 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 -- Ch. 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 -- Ch. 12. The Role of the Critical Orbit. 12.1. The Schwarzian Derivative. 12.2. The Critical Point and Basins of Attraction -- Ch. 13. Newton's Method. 13.1. Basic Properties. 13.2. Convergence and Nonconvergence -- ".
catalog description "Includes bibliographical references (p. 295-298) and index.".
catalog extent "xi, 302 p. :".
catalog identifier "0201554062".
catalog isPartOf "Addison-Wesley studies in nonlinearity.".
catalog isPartOf "Studies in nonlinearity".
catalog issued "1992".
catalog issued "c1992.".
catalog language "eng".
catalog publisher "Reading, Mass. : Addison-Wesley,".
catalog subject "515/.352 20".
catalog subject "Chaotic behavior in systems.".
catalog subject "Differentiable dynamical systems.".
catalog subject "QA614.8 .D49 1992".
catalog tableOfContents "Ch. 1. A Mathematical and Historical Tour. 1.1. Images from Dynamical Systems. 1.2. A Brief History of Dynamics -- Ch. 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 -- Ch. 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 -- Ch. 4. Graphical Analysis. 4.1. Graphical Analysis. 4.2. Orbit Analysis. 4.3. The Phase Portrait -- Ch. 5. Fixed and Periodic Points. 5.1. 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 -- Ch. 6. Bifurcations. 6.1. Dynamics of the Quadratic Map. 6.2. The Saddle-Node Bifurcation. 6.3. The Period-Doubling Bifurcation. 6.4. Experiment: The Transition to Chaos -- ".
catalog tableOfContents "Ch. 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 -- Ch. 15. Complex Functions. 15.1. Complex Arithmetic. 15.2. Complex Square Roots. 15.3. Linear Complex Functions. 15.4. Calculus of Complex Functions -- Ch. 16. The Julia Set. 16.1. The Squaring Function. 16.2. The Chaotic Quadratic Function. 16.3. Cantor Sets Again. 16.4. Computing the Filled Julia Set. 16.5. Experiment: Filled Julia Sets and Critical Orbits. 16.6. The Julia Set as a Repellor -- Ch. 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 -- ".
catalog tableOfContents "Ch. 18. Further Projects and Experiments. 18.1. The Tricorn. 18.2. Cubics. 18.3. Exponential Functions. 18.4. Trigonometric Functions. 18.5. Complex Newton's Method -- Appendix A. Mathematical Preliminaries -- Appendix B. Algorithms -- Appendix C. References.".
catalog tableOfContents "Ch. 7. The Quadratic Family. 7.1. The Case c = -2. 7.2. The Case c [actual symbol not reproducible] -2. 7.3. The Cantor Middle-Thirds Set -- Ch. 8. Transition to Chaos. 8.1. The Orbit Diagram. 8.2. The Period-Doubling Route to Chaos. 8.3. Experiment: Windows in the Orbit Diagram -- Ch. 9. Symbolic Dynamics. 9.1. Itineraries. 9.2. The Sequence Space. 9.3. The Shift Map. 9.4. Conjugacy -- Ch. 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 -- Ch. 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 -- Ch. 12. The Role of the Critical Orbit. 12.1. The Schwarzian Derivative. 12.2. The Critical Point and Basins of Attraction -- Ch. 13. Newton's Method. 13.1. Basic Properties. 13.2. Convergence and Nonconvergence -- ".
catalog title "A first course in chaotic dynamical systems : theory and experiment / Robert L. Devaney.".
catalog type "text".