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Product Code:  MMONO/146 
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Electronic ISBN:  9781470445638 
Product Code:  MMONO/146.E 
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Book DetailsTranslations of Mathematical MonographsVolume: 146; 1995; 204 ppMSC: Primary 34;
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.Introduction to Linear Systems of Differential Equations presents the proof of the necessary and sufficient conditions for stability of the exponents for the simplest case of a twodimensional diagonal system.ReadershipGraduate students and research mathematicians interested in the theory of differential equations.

Table of Contents

Chapters

Chapter I. Linear autonomous and periodic systems

Chapter II. Lyapunov characteristic exponents in the theory of linear systems

Chapter III. Reducible, almost reducible, and regular systems

Chapter IV. Stability and small perturbations of the coefficients of linear systems

Chapter V. On the variation of characteristic exponents under small perturbations of coefficients

Chapter VI. A linear homogeneous equation of the second order


Reviews

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


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

Chapters

Chapter I. Linear autonomous and periodic systems

Chapter II. Lyapunov characteristic exponents in the theory of linear systems

Chapter III. Reducible, almost reducible, and regular systems

Chapter IV. Stability and small perturbations of the coefficients of linear systems

Chapter V. On the variation of characteristic exponents under small perturbations of coefficients

Chapter VI. A linear homogeneous equation of the second order

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