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.
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.
Auteur Richard A. Holmgren
Date de publication 17.08.2000
Nombre de pages 223
Type de produit Livre de Poche
Dimension 235 x 175 x 155 mm
Poids du produit 770 g
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