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Softcover ISBN:  9780821847732 
Product Code:  MMONO/66.S 
List Price:  $165.00 
MAA Member Price:  $148.50 
AMS Member Price:  $132.00 
eBook ISBN:  9781470444808 
Product Code:  MMONO/66.E 
List Price:  $155.00 
MAA Member Price:  $139.50 
AMS Member Price:  $124.00 
Softcover ISBN:  9780821847732 
eBook ISBN:  9781470444808 
Product Code:  MMONO/66.S.B 
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MAA Member Price:  $288.00 $218.25 
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Book DetailsTranslations of Mathematical MonographsVolume: 66; 1986; 435 ppMSC: Primary 58; Secondary 34
Over the past two decades the theory of limit cycles, especially for quadratic differential systems, has progressed dramatically in China as well as in other countries. This monograph, updating the 1964 first edition, includes these recent developments, as revised by eight of the author's colleagues in their own areas of expertise.
The first part of the book deals with limit cycles of general plane stationary systems, including their existence, nonexistence, stability, and uniqueness. The second section discusses the global topological structure of limit cycles and phaseportraits of quadratic systems. Finally, the last section collects important results that could not be included under the subject matter of the previous two sections or that have appeared in the literature very recently. The book as a whole serves as a reference for college seniors, graduate students, and researchers in mathematics and physics.

Table of Contents

Chapters

Introduction

Fundamental Concepts, Concrete Examples, and Several Criteria to Establish Existence and Nonexistence of Limit Cycles

Multiplicity and Stability of Limit Cycles

Limit Cycles in Rotated Vector Fields

General Behavior of Limit Cycles Depending on a Parameter

Existence of a Limit Cycle

Uniqueness of a Limit Cycle

Existence of Several Limit Cycles

Structural Stability of Differential Systems

Work of M. Frommer and N. N. Bautin

Global Structural Analysis of Some Quadratic Systems without Limit Cycles

General Properties and Relative Positions of Limit Cycles in Quadratic Differential Systems

Classification of Quadratic Differential Systems. Limit Cycles of Equations of Class I

Global Structure of Trajectories of Equations of Class II without Limit Cycles

Relative Positions of Limit Cycles and Conditions for Having at Most One and Two Limit Cycles in Equations of Class II

Some Local and Global Properties of Equations of Class III

The Method of Dulac Functions in the Qualitative Study of Quadratic Systems

Limit Cycles in Bounded Quadratic Systems

Appendix


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Over the past two decades the theory of limit cycles, especially for quadratic differential systems, has progressed dramatically in China as well as in other countries. This monograph, updating the 1964 first edition, includes these recent developments, as revised by eight of the author's colleagues in their own areas of expertise.
The first part of the book deals with limit cycles of general plane stationary systems, including their existence, nonexistence, stability, and uniqueness. The second section discusses the global topological structure of limit cycles and phaseportraits of quadratic systems. Finally, the last section collects important results that could not be included under the subject matter of the previous two sections or that have appeared in the literature very recently. The book as a whole serves as a reference for college seniors, graduate students, and researchers in mathematics and physics.

Chapters

Introduction

Fundamental Concepts, Concrete Examples, and Several Criteria to Establish Existence and Nonexistence of Limit Cycles

Multiplicity and Stability of Limit Cycles

Limit Cycles in Rotated Vector Fields

General Behavior of Limit Cycles Depending on a Parameter

Existence of a Limit Cycle

Uniqueness of a Limit Cycle

Existence of Several Limit Cycles

Structural Stability of Differential Systems

Work of M. Frommer and N. N. Bautin

Global Structural Analysis of Some Quadratic Systems without Limit Cycles

General Properties and Relative Positions of Limit Cycles in Quadratic Differential Systems

Classification of Quadratic Differential Systems. Limit Cycles of Equations of Class I

Global Structure of Trajectories of Equations of Class II without Limit Cycles

Relative Positions of Limit Cycles and Conditions for Having at Most One and Two Limit Cycles in Equations of Class II

Some Local and Global Properties of Equations of Class III

The Method of Dulac Functions in the Qualitative Study of Quadratic Systems

Limit Cycles in Bounded Quadratic Systems

Appendix