Author | Holmgren, Richard A. author |
---|---|
Title | A First Course in Discrete Dynamical Systems [electronic resource] / by Richard A. Holmgren |
Imprint | New York, NY : Springer New York : Imprint: Springer, 1996 |
Edition | Second Edition |
Connect to | http://dx.doi.org/10.1007/978-1-4419-8732-7 |
Descript | XV, 223 p. 4 illus. online resource |
1.1. Phase Portraits -- Exercise Set 1 -- A Quick Look at Functions -- Exercise Set 2 -- The Topology of the Real Numbers -- Exercise Set 3 -- Periodic Points and Stable Sets -- 4.1 Graphical Analysis -- Sarkovskii's Theorem -- Exercise Set 5 -- Differentiability and Its Implications -- Exercise Set 6 -- Parametrized Families of Functions and Bifurcations -- Exercise Set 7 -- The Logistic Function Part I: 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 -- The Logistic Function Part II: Topological Conjugacy -- Exercise Set 9 -- The Logistic Function Part III: A Period-Doubling Cascade -- Exercise Set 10 -- The Logistic Function Part IV: Symbolic Dynamics -- 11.1. Symbolic Dynamics and Metric Spaces -- 11.2. Symbolic Dynamics and the Logistic Function -- 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 -- Numerical Solutions of Differential Equations -- Exercise Set 13 -- 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 -- The Quadratic Family and the Mandelbrot Set -- 15.1 Generating Julia and Mandelbrot Sets on a Computer -- A.l. 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 -- General Interest Books on Dynamics -- Topics in Mathematics -- Computer Programs and Algorithms