**Pure and Applied Undergraduate Texts**

Volume: 19;
2012;
733 pp;
Hardcover

MSC: Primary 34; 37; 70;

Print ISBN: 978-0-8218-9135-3

Product Code: AMSTEXT/19

List Price: $93.00

Individual Member Price: $74.40

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**Electronic ISBN: 978-0-8218-9398-2
Product Code: AMSTEXT/19.E**

List Price: $93.00

Individual Member Price: $74.40

#### Supplemental Materials

# An Introduction to Dynamical Systems: Continuous and Discrete, Second Edition

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*R. Clark Robinson*

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

# Table of Contents

## An Introduction to Dynamical Systems: Continuous and Discrete, Second Edition

- Cover Cover11 free
- Title page iii4 free
- Contents vii8 free
- Prefaces xiii14 free
- Historical prologue xvii18 free
- Part I. Systems of nonlinear differential equations 122 free
- Geometric approach to differential equations 324
- Linear systems 1132
- The flow: Solutions of nonlinear equations 7596
- Phase portraits with emphasis on fixed points 109130
- Phase portraits using Scalar functions 169190
- Periodic orbits 213234
- Chaotic attractors 285306
- Part II. Iteration of functions 341362
- Iteration of functions as dynamics 343364
- Periodic points of one-dimensional maps 353374
- Itineraries for one-dimensional maps 423444
- Invariant sets for one-dimensional maps 487508
- Periodic points of higher dimensional maps 541562
- Invariant sets for higher dimensional maps 597618
- Fractals 669690
- Background and terminology 705726
- Generic properties 717738
- Bibliography 721742
- Index 727748 free
- Back Cover Back Cover1762