Author | Holmgren, Richard A. author |
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Title | A First Course in Discrete Dynamical Systems [electronic resource] / by Richard A. Holmgren |
Imprint | New York, NY : Springer US, 1994 |
Connect to | http://dx.doi.org/10.1007/978-1-4684-0222-3 |
Descript | XII, 214 p. online resource |
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 Periodic Points and Stable Sets -- 4.1 Graphical Analysis -- Exercise Set 4 -- 5 Sarkovskiiโs Theorem -- Exercise Set 5 -- 6 Differentiability and Its Implications -- Exercise Set 6 -- 7 Parametrized Families of Functions and Bifurcations -- Exercise Set 7 -- 8 The Logistic Function, Part I -- Exercise Set 8 -- 9 Symbolic Dynamics and Chaos -- Exercise Set 9 -- 10 The Logistic Function, Part II: Topological Conjugacy -- Exercise Set 10 -- 11 The Logistic Function, Part III -- Exercise Set 11 -- 12 Newtonโs Method -- 12.1 Newtonโs Method for Quadratic Functions -- 12.2 Newtonโs Method for Cubic Functions -- 12.3 Intervals and Rates of Convergence -- Exercise Set 12 -- 13 Numerical Solutions of Differential 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 Newtonโs Method in the Complex Plane -- Exercise Set 14 -- 15 The Quadratic Family and the Mandelbrot Set -- Generating Julia and Mandelbrot Sets on a Computer -- Exercise Set 15 -- Appendix A. Computer Algorithms -- A.1 Iterating Functions -- Finding the Value of a Point Under Iteration -- Tables of Iterates -- Controlling the Precision of the Computations -- Graphing Iterated Functions -- A.2 Graphical Analysis -- A.3 Bifurcation Diagrams -- A.4 Julia Sets -- A.5 The Mandelbrot Set -- A.6 Stable Sets of Newtonโs Method -- References -- Dynamical Systems -- Topics in Mathematics -- General Interest Books on Dynamics -- Computer Programs and Algorithms -- List of Symbols