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Limit Cycles of Differential Equations

  • Textbook
  • © 2007

Overview

Authors:
  1. Colin Christopher

    1. School of Mathematics and Statistics, University of Plymouth, Plymouth, UK

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    You can also search for this author in PubMed   Google Scholar

  2. Chengzhi Li

    1. School of Mathematical Sciences, Beijing University, Beijing, China

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    You can also search for this author in PubMed   Google Scholar

  • Gives a survey of current areas of active research
  • Written in an approachable manner suitable for graduate students
  • Includes supplementary material: sn.pub/extras

Part of the book series: Advanced Courses in Mathematics - CRM Barcelona (ACMBIRK)

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Table of contents (14 chapters)

  1. Front Matter

    Pages i-viii
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  2. Around the Center-Focus Problem

    1. Front Matter

      Pages 1-3
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    2. Centers and Limit Cycles

      Pages 5-15

    3. Darboux Integrability

      Pages 17-23

    4. Liouvillian Integrability

      Pages 25-31

    5. Symmetry

      Pages 33-39

    6. Cherkas’ Systems

      Pages 41-48

    7. Monodromy

      Pages 49-54

    8. The Tangential Center-Focus Problem

      Pages 55-61

    9. Monodromy of Hyperelliptic Abelian Integrals

      Pages 63-69

    10. Holonomy and the Lotka-Volterra System

      Pages 71-78

    11. Other Approaches

      Pages 79-84

  3. Back Matter

    Pages 85-89
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  4. Abelian Integrals and Applications to the Weak Hilbert’s 16th Problem

    1. Front Matter

      Pages 91-93
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    2. Hilbert’s 16th Problem and Its Weak Form

      Pages 95-109

    3. Abelian Integrals and Limit Cycles

      Pages 111-126

    4. Estimate of the Number of Zeros of Abelian Integrals

      Pages 127-142

    5. A Unified Proof of the Weak Hilbert’s 16th Problem for n=2

      Pages 143-158

  5. Back Matter

    Pages 159-171
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Keywords

About this book

This textbook contains the lecture series originally delivered at the "Advanced Course on Limit Cycles of Differential Equations" in the Centre de Recerca Matemàtica Barcelona in 2006.

The topics covered are the center-focus problem for polynomial vector fields, and the application of abelian integrals to limit cycle bifurcations. Both topics are related to Hilbert's sixteenth problem. In particular, the book will be of interest to students and researchers working in the qualitative theory of dynamical systems.

Reviews

“The book is well written and informative, including some recent references. It would be very useful as an introduction to the subject.” (Iliya Iliev, zbMATH 1359.34001, 2017)

Authors and Affiliations

  • School of Mathematics and Statistics, University of Plymouth, Plymouth, UK

    Colin Christopher

  • School of Mathematical Sciences, Beijing University, Beijing, China

    Chengzhi Li

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