An Introduction to Dynamical Systems
Published on 22. April 2004
Book
Hardback
672 pages
978-0-13-143140-9 (ISBN)
Description
For one- or two-semester courses in Dynamical Systems in the department of Advanced Mathematics.
This text gives an introduction into the ideas of dynamical systems. It is divided into two parts which can be treated in either order: the first part treats the aspects coming from systems of nonlinear ordinary differential equations, and the second part is comprised of those aspects dealing with iteration of a function. Its main emphasis is on the types of behavior which nonlinear systems of differential equations can exhibit. The text assumes that students have taken courses on calculus covering both a single variable and multivariables, a course on linear algebra, and an introductory course on differential equations.
This text gives an introduction into the ideas of dynamical systems. It is divided into two parts which can be treated in either order: the first part treats the aspects coming from systems of nonlinear ordinary differential equations, and the second part is comprised of those aspects dealing with iteration of a function. Its main emphasis is on the types of behavior which nonlinear systems of differential equations can exhibit. The text assumes that students have taken courses on calculus covering both a single variable and multivariables, a course on linear algebra, and an introductory course on differential equations.
More details
Language
English
Place of publication
United States
Publishing group
Pearson Education (US)
Target group
Professional and scholarly
Dimensions
Height: 210 mm
Width: 259 mm
Thickness: 28 mm
Weight
1266 gr
ISBN-13
978-0-13-143140-9 (9780131431409)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
New editions
Open Software Foundation
OSF/Midget Widget Writing Gde
Book
04/1995
Longman Higher Education
€37.08
Article is exhausted; no reprint
Content
(NOTE: Each chapter concludes with Applications, Theory and Proofs, and Exercises.)
Prologue: Historical Perspective.
I. SYSTEMS OF DIFFERENTIAL EQUATIONS.
1. Geometric Approach to Differential Equations.
2. Linear Systems.
3. The Flow: Solutions of Nonlinear Equations.
4. Phase Portraits with Emphasis on Fixed Points.
5. Phase Portraits Using Energy and Other Test Functions.
6. Periodic Orbits.
7. Chaotic Attractors.
II. ITERATION OF FUNCTIONS.
8. Iteration of Functions as Dynamics.
9. Periodic Points of One-Dimensional Maps.
10. Itineraries for One-Dimensional Maps.
11. Invariant Sets for One-Dimensional Maps.
12. Periodic Points of Higher Dimensional Maps.
13. Invariant Sets for Higher Dimensional Maps.
14. Fractals.
Appendix A: Calculus Background.
Appendix B: Analysis and Topology Terminology.
Appendix C: Linear Algebra Background.
Bibliography.
Index.
Prologue: Historical Perspective.
I. SYSTEMS OF DIFFERENTIAL EQUATIONS.
1. Geometric Approach to Differential Equations.
2. Linear Systems.
3. The Flow: Solutions of Nonlinear Equations.
4. Phase Portraits with Emphasis on Fixed Points.
5. Phase Portraits Using Energy and Other Test Functions.
6. Periodic Orbits.
7. Chaotic Attractors.
II. ITERATION OF FUNCTIONS.
8. Iteration of Functions as Dynamics.
9. Periodic Points of One-Dimensional Maps.
10. Itineraries for One-Dimensional Maps.
11. Invariant Sets for One-Dimensional Maps.
12. Periodic Points of Higher Dimensional Maps.
13. Invariant Sets for Higher Dimensional Maps.
14. Fractals.
Appendix A: Calculus Background.
Appendix B: Analysis and Topology Terminology.
Appendix C: Linear Algebra Background.
Bibliography.
Index.