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An Introduction to Dynamical Systems: Continuous and Discrete, Second Edition
 
R. Clark Robinson Northwestern University, Evanston, IL
An Introduction to Dynamical Systems
An Introduction to Dynamical Systems
Hardcover ISBN:  978-0-8218-9135-3
Product Code:  AMSTEXT/19
List Price: $99.00
MAA Member Price: $89.10
AMS Member Price: $79.20
Sale Price: $64.35
eBook ISBN:  978-0-8218-9398-2
Product Code:  AMSTEXT/19.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Sale Price: $55.25
Hardcover ISBN:  978-0-8218-9135-3
eBook: ISBN:  978-0-8218-9398-2
Product Code:  AMSTEXT/19.B
List Price: $184.00$141.50
MAA Member Price: $165.60$127.35
AMS Member Price: $147.20$113.20
Sale Price: $119.60$91.98
An Introduction to Dynamical Systems
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An Introduction to Dynamical Systems
An Introduction to Dynamical Systems: Continuous and Discrete, Second Edition
R. Clark Robinson Northwestern University, Evanston, IL
Hardcover ISBN:  978-0-8218-9135-3
Product Code:  AMSTEXT/19
List Price: $99.00
MAA Member Price: $89.10
AMS Member Price: $79.20
Sale Price: $64.35
eBook ISBN:  978-0-8218-9398-2
Product Code:  AMSTEXT/19.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Sale Price: $55.25
Hardcover ISBN:  978-0-8218-9135-3
eBook ISBN:  978-0-8218-9398-2
Product Code:  AMSTEXT/19.B
List Price: $184.00$141.50
MAA Member Price: $165.60$127.35
AMS Member Price: $147.20$113.20
Sale Price: $119.60$91.98
  • Book Details
     
     
    Pure and Applied Undergraduate Texts
    Volume: 192012; 733 pp
    MSC: Primary 34; 37; 70;

    This book gives a mathematical treatment of the introduction to qualitative differential equations and discrete dynamical systems. The treatment includes theoretical proofs, methods of calculation, and applications. The two parts of the book, continuous time of differential equations and discrete time of dynamical systems, can be covered independently in one semester each or combined together into a year long course.

    The material on differential equations introduces the qualitative or geometric approach through a treatment of linear systems in any dimension. There follows chapters where equilibria are the most important feature, where scalar (energy) functions is the principal tool, where periodic orbits appear, and finally, chaotic systems of differential equations. The many different approaches are systematically introduced through examples and theorems.

    The material on discrete dynamical systems starts with maps of one variable and proceeds to systems in higher dimensions. The treatment starts with examples where the periodic points can be found explicitly and then introduces symbolic dynamics to analyze where they can be shown to exist but not given in explicit form. Chaotic systems are presented both mathematically and more computationally using Lyapunov exponents. With the one-dimensional maps as models, the multidimensional maps cover the same material in higher dimensions. This higher dimensional material is less computational and more conceptual and theoretical. The final chapter on fractals introduces various dimensions which is another computational tool for measuring the complexity of a system. It also treats iterated function systems which give examples of complicated sets.

    In the second edition of the book, much of the material has been rewritten to clarify the presentation. Also, some new material has been included in both parts of the book.

    This book can be used as a textbook for an advanced undergraduate course on ordinary differential equations and/or dynamical systems. Prerequisites are standard courses in calculus (single variable and multivariable), linear algebra, and introductory differential equations.

    Readership

    Undergraduate and graduate students interested in dynamical systems.

  • Table of Contents
     
     
    • Cover
    • Title page
    • Contents
    • Prefaces
    • Historical prologue
    • Part I. Systems of nonlinear differential equations
    • Geometric approach to differential equations
    • Linear systems
    • The flow: Solutions of nonlinear equations
    • Phase portraits with emphasis on fixed points
    • Phase portraits using Scalar functions
    • Periodic orbits
    • Chaotic attractors
    • Part II. Iteration of functions
    • Iteration of functions as dynamics
    • Periodic points of one-dimensional maps
    • Itineraries for one-dimensional maps
    • Invariant sets for one-dimensional maps
    • Periodic points of higher dimensional maps
    • Invariant sets for higher dimensional maps
    • Fractals
    • Background and terminology
    • Generic properties
    • Bibliography
    • Index
    • Back Cover
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Desk Copy – for instructors who have adopted an AMS textbook for a course
    Examination Copy – for faculty considering an AMS textbook for a course
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 192012; 733 pp
MSC: Primary 34; 37; 70;

This book gives a mathematical treatment of the introduction to qualitative differential equations and discrete dynamical systems. The treatment includes theoretical proofs, methods of calculation, and applications. The two parts of the book, continuous time of differential equations and discrete time of dynamical systems, can be covered independently in one semester each or combined together into a year long course.

The material on differential equations introduces the qualitative or geometric approach through a treatment of linear systems in any dimension. There follows chapters where equilibria are the most important feature, where scalar (energy) functions is the principal tool, where periodic orbits appear, and finally, chaotic systems of differential equations. The many different approaches are systematically introduced through examples and theorems.

The material on discrete dynamical systems starts with maps of one variable and proceeds to systems in higher dimensions. The treatment starts with examples where the periodic points can be found explicitly and then introduces symbolic dynamics to analyze where they can be shown to exist but not given in explicit form. Chaotic systems are presented both mathematically and more computationally using Lyapunov exponents. With the one-dimensional maps as models, the multidimensional maps cover the same material in higher dimensions. This higher dimensional material is less computational and more conceptual and theoretical. The final chapter on fractals introduces various dimensions which is another computational tool for measuring the complexity of a system. It also treats iterated function systems which give examples of complicated sets.

In the second edition of the book, much of the material has been rewritten to clarify the presentation. Also, some new material has been included in both parts of the book.

This book can be used as a textbook for an advanced undergraduate course on ordinary differential equations and/or dynamical systems. Prerequisites are standard courses in calculus (single variable and multivariable), linear algebra, and introductory differential equations.

Readership

Undergraduate and graduate students interested in dynamical systems.

  • Cover
  • Title page
  • Contents
  • Prefaces
  • Historical prologue
  • Part I. Systems of nonlinear differential equations
  • Geometric approach to differential equations
  • Linear systems
  • The flow: Solutions of nonlinear equations
  • Phase portraits with emphasis on fixed points
  • Phase portraits using Scalar functions
  • Periodic orbits
  • Chaotic attractors
  • Part II. Iteration of functions
  • Iteration of functions as dynamics
  • Periodic points of one-dimensional maps
  • Itineraries for one-dimensional maps
  • Invariant sets for one-dimensional maps
  • Periodic points of higher dimensional maps
  • Invariant sets for higher dimensional maps
  • Fractals
  • Background and terminology
  • Generic properties
  • Bibliography
  • Index
  • Back Cover
Review Copy – for publishers of book reviews
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.