| Preface Rationale for the new edition How to use this book. Acknowledgments. List of Symbols 1.Introduction 1.1.Phase Portraits Exercise Set 1. 2.A Quick Look at Functions Exercise Set 2. 3.The Topology of the Real Numbers Exercise Set 3 4.Perlodic Points and Stable Sets 4.1.Graphical Analysis Exercise Set 4. 5.Sarkovskii’S Theorem Exercise Set 5. 6.Differentiability and Its Implications Exercise Set 6. 7.Parametrized Farallies of Functions and Bifurcations Exercise Set 7 8.The Logistic Function Part l：Cantor Sets and Chaos 8.1.A First Look at the Logistic Function when r>4 8.2.Cantor Sets. 8.3.Chaos and the Dynamics of the Logistic Function 8.4.A Few Additional Comments on Cantor Sets Exercise Set 8 9.The Logistic Function Part Il：Topological Conjugacy Exercise Set 9 10.The Logistic Function Part IIl：A Period-Doubling C：ascade Exercise Set 10. 11.The Logistic Function Part IV：Symbolic Dynamics 11.1.Symbolic Dynamics and Metric Spaces 1 1.2.Symbolic Dynamics and the Logistic Function Exercise Set 11. 12.Newton’S Method 12.1.Newton’S Method for Quadratic Functions 12.2.Newton’S Method for Cubic Functions 12.3.Intervals and Rates of Convergence Exercise Set 12. 13.Numerical Solutions of Diffrential Equations Exercise Set 13. 14.The Dynamics of Complex Functions 14.1.The Complex Numbers. 14.2.Complex Functions， 14.3.The Dynamics of Complex FUnctions. 14.4.The Riemann Sphere 14.5.Newton’S Method in the Complex Plane Exercise Set 14. 15.The Quadratic Family and the Mandelbrot Set 15.1.Generating Julia and Mandelbrot Sets on a Computer. Exercise Set 15 Appendix.Mathematica Algorithms A.1.Iterating FUnctions. Finding the VaIue of a Point Under Iteration Tables of Iterates …… References Index |
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