**Translations of Mathematical Monographs**

1995;
204 pp;
Hardcover

MSC: Primary 34;

Print ISBN: 978-0-8218-0328-8

Product Code: MMONO/146

List Price: $98.00

AMS Member Price: $78.40

MAA Member Price: $88.20

**Electronic ISBN: 978-1-4704-4563-8
Product Code: MMONO/146.E**

List Price: $98.00

AMS Member Price: $78.40

MAA Member Price: $88.20

# Introduction to Linear Systems of Differential Equations

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*L. Ya. Adrianova*

The theory of linear systems of differential equations is
one of the cornerstones of the whole theory of differential equations.
At its root is the concept of the Lyapunov characteristic exponent.

In this book, Adrianova presents introductory material and
further detailed discussions of Lyapunov exponents. She also discusses
the structure of the space of solutions of linear systems. Classes
of linear systems examined are from the narrowest to
widest: 1) autonomous, 2) periodic, 3) reducible to
autonomous, 4) nearly reducible to autonomous, 5) regular.

In addition, Adrianova considers the
following:

- stability of linear systems and the influence of perturbations of the coefficients on the stability
- the criteria of uniform stability and of uniform asymptotic stability in terms of properties of the solutions
- several estimates of the growth rate of solutions of a linear system in terms of its coefficients

How perturbations of the coefficients change all the elements of the spectrum of the system is definitely the most complicated and involved problem in the whole theory of linear systems.

#### Readership

Graduate students and research mathematicians interested in the theory of differential equations.

#### Reviews & Endorsements

Gives a very good introduction to the theory of linear systems of differential equations … One of the best features of the book is the very large number of examples … suitable for research and graduate students working in the theory of differential equations and in mathematical applications … gives a good foundation for the study of more involved and specialized parts of the theory of linear differential equations.

-- Zentralblatt MATH

#### Table of Contents

# Table of Contents

## Introduction to Linear Systems of Differential Equations

- Cover Cover11
- Title page iii4
- Contents v6
- Preface vii8
- Principal notation ix10
- Chapter I. Linear autonomous and periodic systems 112
- Chapter II. Lyapunov characteristic exponents in the theory of linear systems 2536
- Chapter III. Reducible, almost reducible, and regular systems 4354
- Chapter IV. Stability and small perturbations of the coefficients of linear systems 7990
- Chapter V. On the variation of characteristic exponents under small perturbations of coefficients 121132
- Chapter VI. A linear homogeneous equation of the second order 175186
- Appendix 197208
- References 201212
- Index 203214
- Back Cover Back Cover1218