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Description

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.

Observation

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.

Contributeurs

Auteur Richard A. Holmgren

Détails sur le produit

DUIN 18PQ8NT2CRV

GTIN 9780387947808

Date de publication 17.08.2000

Langues Anglais

Nombre de pages 223

Type de produit Livre de Poche

Dimension 235 x 175 x 155  mm

Poids du produit 770 g

A First Course in Discrete Dynamical Systems

Richard A. Holmgren

51,93 €

Vendeur: Dodax EU

Date de livraison: entre jeudi, 30. août et lundi, 3. septembre

État: Neuf

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51,93 €
TVA incluse - Livraison GRATUITE