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Structurally Stable Quadratic Vector Fields
 
Joan C. Artés Universitat Autonoma de Barcelona, Barcelona, Spain
Robert E. Kooij Technische Universiteit Delft, Delft, Netherlands
Jaume Llibre Universitat Autonoma de Barcelona, Barcelona, Spain
Structurally Stable Quadratic Vector Fields
eBook ISBN:  978-1-4704-0228-0
Product Code:  MEMO/134/639.E
List Price: $49.00
MAA Member Price: $44.10
AMS Member Price: $29.40
Structurally Stable Quadratic Vector Fields
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Structurally Stable Quadratic Vector Fields
Joan C. Artés Universitat Autonoma de Barcelona, Barcelona, Spain
Robert E. Kooij Technische Universiteit Delft, Delft, Netherlands
Jaume Llibre Universitat Autonoma de Barcelona, Barcelona, Spain
eBook ISBN:  978-1-4704-0228-0
Product Code:  MEMO/134/639.E
List Price: $49.00
MAA Member Price: $44.10
AMS Member Price: $29.40
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 1341998; 108 pp
    MSC: Primary 34; 58

    This book solves a problem that has been open for over 20 years—the complete classification of structurally stable quadratic vector fields modulo limit cycles. The 1950s saw the first real impetus given to the development of the qualitative theory of quadratic vector fields, although prior and ongoing interest in the topic can be shown by the more than 800 papers that have been published on the subject. One of the problems in the qualitative theory of quadratic vector fields is the classification of all structurally stable ones: In this work the authors solve this problem completely modulo limit cycles and give all possible phase portraits for such structurally stable quadratic vector fields.

    Readership

    Research mathematicians and graduate students interested in qualitative theory of planar differential equations; physicists and engineers interested in dynamical systems.

  • Table of Contents
     
     
    • Chapters
    • 1. Introduction
    • 2. Preliminary definitions
    • 3. Structural stability theorems
    • 4. Some preliminary tools
    • 5. Proof of Theorem 1.1(a)
    • 6. Proof of Theorem 1.1(b)
    • 7. Proofs of Theorems 1.2, 1.3 and 1.4
    • 8. Structural stability and the parameter space
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 1341998; 108 pp
MSC: Primary 34; 58

This book solves a problem that has been open for over 20 years—the complete classification of structurally stable quadratic vector fields modulo limit cycles. The 1950s saw the first real impetus given to the development of the qualitative theory of quadratic vector fields, although prior and ongoing interest in the topic can be shown by the more than 800 papers that have been published on the subject. One of the problems in the qualitative theory of quadratic vector fields is the classification of all structurally stable ones: In this work the authors solve this problem completely modulo limit cycles and give all possible phase portraits for such structurally stable quadratic vector fields.

Readership

Research mathematicians and graduate students interested in qualitative theory of planar differential equations; physicists and engineers interested in dynamical systems.

  • Chapters
  • 1. Introduction
  • 2. Preliminary definitions
  • 3. Structural stability theorems
  • 4. Some preliminary tools
  • 5. Proof of Theorem 1.1(a)
  • 6. Proof of Theorem 1.1(b)
  • 7. Proofs of Theorems 1.2, 1.3 and 1.4
  • 8. Structural stability and the parameter space
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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