A first course in discrete dynamical systems / Richard A. Holmgren.

By:

Holmgren, Richard A

Material type: Text

TextSeries: UniversitextPublication details: New York : Springer, c1996.Edition: 2nd edDescription: xv, 223 p. : ill. ; 24 cmISBN:

9780387947808

Subject(s):

Differentiable dynamical systems

DDC classification:

514.74 20 HOL

LOC classification:

QA614.8 .H65 1996

Online resources:

Contents:

Introduction Richard A. Holmgren Pages 1-8 A Quick Look at Functions Richard A. Holmgren Pages 9-20 The Topology of the Real Numbers Richard A. Holmgren Pages 21-29 Periodic Points and Stable Sets Richard A. Holmgren Pages 31-39 Sarkovskii’s Theorem Richard A. Holmgren Pages 41-46 Differentiability and Its Implications Richard A. Holmgren Pages 47-57 Parametrized Families of Functions and Bifurcations Richard A. Holmgren Pages 59-67 The Logistic Function Part I: Cantor Sets and Chaos Richard A. Holmgren Pages 69-86 The Logistic Function Part II: Topological Conjugacy Richard A. Holmgren Pages 87-93 The Logistic Function Part III: A Period-Doubling Cascade Richard A. Holmgren Pages 95-108 The Logistic Function Part IV: Symbolic Dynamics Richard A. Holmgren Pages 109-126 Newton’s Method Richard A. Holmgren Pages 127-151 Numerical Solutions of Differential Equations Richard A. Holmgren Pages 153-165 The Dynamics of Complex Functions Richard A. Holmgren Pages 167-192 The Quadratic Family and the Mandelbrot Set Richard A. Holmgren Pages 193-202 Back Matter Pages 203-224

Summary: 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.

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Holdings
Item type	Current library	Collection	Call number	Status	Date due	Barcode
Project book	CUTN Central Library	Non-fiction	514.74 HOL (Browse shelf(Opens below))	Checked out to Renuka Devi V (20019T)	31/01/2024	48807

Includes bibliographical references (p. [215]-220) and index.

Introduction
Richard A. Holmgren
Pages 1-8
A Quick Look at Functions
Richard A. Holmgren
Pages 9-20
The Topology of the Real Numbers
Richard A. Holmgren
Pages 21-29
Periodic Points and Stable Sets
Richard A. Holmgren
Pages 31-39
Sarkovskii’s Theorem
Richard A. Holmgren
Pages 41-46
Differentiability and Its Implications
Richard A. Holmgren
Pages 47-57
Parametrized Families of Functions and Bifurcations
Richard A. Holmgren
Pages 59-67
The Logistic Function Part I: Cantor Sets and Chaos
Richard A. Holmgren
Pages 69-86
The Logistic Function Part II: Topological Conjugacy
Richard A. Holmgren
Pages 87-93
The Logistic Function Part III: A Period-Doubling Cascade
Richard A. Holmgren
Pages 95-108
The Logistic Function Part IV: Symbolic Dynamics
Richard A. Holmgren
Pages 109-126
Newton’s Method
Richard A. Holmgren
Pages 127-151
Numerical Solutions of Differential Equations
Richard A. Holmgren
Pages 153-165
The Dynamics of Complex Functions
Richard A. Holmgren
Pages 167-192
The Quadratic Family and the Mandelbrot Set
Richard A. Holmgren
Pages 193-202
Back Matter
Pages 203-224

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.

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