A First Course in Discrete Dynamical Systems (Universitext)

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9780387947808: A First Course in Discrete Dynamical Systems (Universitext)
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Given the ease with which computers can do iteration it is now possible for almost anyone to generate beautiful images whose roots lie in discrete dynamical systems. Images of Mandelbrot and Julia sets abound in publications both mathematical and not. The mathematics behind the pictures are beautiful in their own right and are the subject of this text. Mathematica programs that illustrate the dynamics are included in an appendix.

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A discrete dynamical system can be characterized as an iterated function. Given the efficiency with which computers can do iteration, it is now possible for anyone with access to a personal computer to generate beautiful images whose roots lie in discrete dynamical systems. Images of Mandelbrot and Julia sets abound in publications both mathematical and not. The mathematics behind the pictures is beautiful in its own right and is the subject of this text. The level of presentation is suitable for advanced undergraduates who have completed a year of college-level calculus. Concepts from calculus are reviewed as necessary. Mathematica programs that illustrate the dynamics and that will aid the student in doing the exercises are included in the Appendix. In this second edition, the topics covered are rearranged to make the text more flexible. In particular, the material on symbolic dynamics is now optional, and the book can easily be used for a single-semester course dealing exclusively with functions of a single real variable. Alternatively, the basic properties of dynamical systems can be introduced using functions of a real variable, and then the reader can skip directly to the material on the dynamics of complex functions. Additional changes include the simplification of several proofs, a thorough review and expansion of the exercises, and substantial improvement in the efficiency of the Mathematica programs.

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Richard A. Holmgren
Published by Springer-Verlag New York Inc., United States (2000)
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Book Description Springer-Verlag New York Inc., United States, 2000. Paperback. Condition: New. 2nd ed. 1996. Corr. 2nd printing 2000. Language: English . Brand New Book. Given the ease with which computers can do iteration it is now possible for almost anyone to generate beautiful images whose roots lie in discrete dynamical systems. Images of Mandelbrot and Julia sets abound in publications both mathematical and not. The mathematics behind the pictures are beautiful in their own right and are the subject of this text. Mathematica programs that illustrate the dynamics are included in an appendix. Seller Inventory # KNV9780387947808

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Book Description Springer-Verlag New York Inc., 2000. PAP. Condition: New. New Book. Shipped from US within 10 to 14 business days. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Seller Inventory # IQ-9780387947808

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Book Description Condition: New. Publisher/Verlag: Springer, Berlin | This book is intended to introduce the reader both to topics in dynamical systems and mathematical thinking. In particular, the authors emphasize those portions of mathematical analysis necessary for understanding the intricacies of a discrete dynamical system. The organizing principle is the development of an understanding of the parametrized family of functions h(x) = rx(1-x). The readers should have some background in calculus though they need not have an extensive background in proof based mathematics. Students will learn to understand periodic points, stable sets, bifurcations, symbolic dynamics, chaos. This book includes rigorous proofs of important concepts in dynamics and is still accessible to the typical advanced undergraduate student. | Discrete dynamical systems are essentially iterated functions. Given the ease with which computers can do iteration, it is now possible for anyone with access to a personal computer to generate beautiful images whose roots lie in discrete dynamical systems. Images of Mandelbrot and Julia sets abound in publications both mathematical and not. The mathematics behind the pictures are beautiful in their own right and are the subject of this text. The level of the presentation is suitable for advanced undergraduates with a year of calculus behind them. Students in the author's courses using this material have come from numerous disciplines; many have been majors in other disciplines who are taking mathematics courses out of general interest. Concepts from calculus are reviewed as necessary. Mathematica programs that illustrate the dynamics and that will aid the student in doing the exercises are included in an appendix. | 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.- Exercise Set 4.- 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.- Exercise Set 8.- 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.- Exercise Set 11.- 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.- 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.- Exercise Set 14.- The Quadratic Family and the Mandelbrot Set.- 15.1 Generating Julia and Mandelbrot Sets on a Computer.- Exercise Set 15.- 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 Newton's Method.- References.- Dynamical Systems.- General Interest Books on Dynamics.- Topics in Mathematics.- Computer Programs and Algorithms. | Format: Paperback | Language/Sprache: english | 350 gr | 223 pp. Seller Inventory # K9780387947808

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Book Description Springer, 1996. Paperback. Condition: New. 2nd. Seller Inventory # DADAX0387947809

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Book Description Springer-Verlag New York Inc., 2000. PAP. Condition: New. New Book. Delivered from our UK warehouse in 4 to 14 business days. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Seller Inventory # IQ-9780387947808

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A FIRST COURSE IN DISCRETE DYNAMICAL SYSTEMS -
Published by Springer (1996)
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Book Description Springer, 1996. Paperback. Condition: NEW. 9780387947808 This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. For all enquiries, please contact Herb Tandree Philosophy Books directly - customer service is our primary goal. Seller Inventory # HTANDREE0411219

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Book Description Springer Aug 2000, 2000. Taschenbuch. Condition: Neu. Neuware - Discrete dynamical systems are essentially iterated functions. Given the ease with which computers can do iteration, it is now possible for anyone with access to a personal computer to generate beautiful images whose roots lie in discrete dynamical systems. Images of Mandelbrot and Julia sets abound in publications both mathematical and not. The mathematics behind the pictures are beautiful in their own right and are the subject of this text. The level of the presentation is suitable for advanced undergraduates with a year of calculus behind them. Students in the author's courses using this material have come from numerous disciplines; many have been majors in other disciplines who are taking mathematics courses out of general interest. Concepts from calculus are reviewed as necessary. Mathematica programs that illustrate the dynamics and that will aid the student in doing the exercises are included in an appendix. 244 pp. Englisch. Seller Inventory # 9780387947808

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Book Description Springer Aug 2000, 2000. Taschenbuch. Condition: Neu. Neuware - Discrete dynamical systems are essentially iterated functions. Given the ease with which computers can do iteration, it is now possible for anyone with access to a personal computer to generate beautiful images whose roots lie in discrete dynamical systems. Images of Mandelbrot and Julia sets abound in publications both mathematical and not. The mathematics behind the pictures are beautiful in their own right and are the subject of this text. The level of the presentation is suitable for advanced undergraduates with a year of calculus behind them. Students in the author's courses using this material have come from numerous disciplines; many have been majors in other disciplines who are taking mathematics courses out of general interest. Concepts from calculus are reviewed as necessary. Mathematica programs that illustrate the dynamics and that will aid the student in doing the exercises are included in an appendix. 244 pp. Englisch. Seller Inventory # 9780387947808

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