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Concerning the Hilbert 16th Problem
 
Edited by: Yu. Ilyashenko Moscow State University
S. Yakovenko Weizmann Institute of Science
Concerning the Hilbert 16th Problem
Hardcover ISBN:  978-0-8218-0362-2
Product Code:  TRANS2/165
List Price: $175.00
MAA Member Price: $157.50
AMS Member Price: $140.00
eBook ISBN:  978-1-4704-3376-5
Product Code:  TRANS2/165.E
List Price: $165.00
MAA Member Price: $148.50
AMS Member Price: $132.00
Hardcover ISBN:  978-0-8218-0362-2
eBook: ISBN:  978-1-4704-3376-5
Product Code:  TRANS2/165.B
List Price: $340.00 $257.50
MAA Member Price: $306.00 $231.75
AMS Member Price: $272.00 $206.00
Concerning the Hilbert 16th Problem
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Concerning the Hilbert 16th Problem
Edited by: Yu. Ilyashenko Moscow State University
S. Yakovenko Weizmann Institute of Science
Hardcover ISBN:  978-0-8218-0362-2
Product Code:  TRANS2/165
List Price: $175.00
MAA Member Price: $157.50
AMS Member Price: $140.00
eBook ISBN:  978-1-4704-3376-5
Product Code:  TRANS2/165.E
List Price: $165.00
MAA Member Price: $148.50
AMS Member Price: $132.00
Hardcover ISBN:  978-0-8218-0362-2
eBook ISBN:  978-1-4704-3376-5
Product Code:  TRANS2/165.B
List Price: $340.00 $257.50
MAA Member Price: $306.00 $231.75
AMS Member Price: $272.00 $206.00
  • Book Details
     
     
    American Mathematical Society Translations - Series 2
    Advances in the Mathematical Sciences
    Volume: 1651995; 219 pp
    MSC: Primary 34

    This book examines qualitative properties of vector fields in the plane, in the spirit of Hilbert's Sixteenth Problem. Two principal topics explored are bifurcations of limit cycles of planar vector fields and desingularization of singular points for individual vector fields and for analytic families of such fields. In addition to presenting important new developments in this area, this book contains an introductory paper which outlines the general context and describes connections between the papers in the volume. The book will appeal to researchers and graduate students working in the qualitative theory of ordinary differential equations and dynamical systems.

    Readership

    Researchers and graduate students working in the qualitative theory of ordinary differential equations.

  • Table of Contents
     
     
    • Chapters
    • Yu. Ilyashenko and S. Yakovenko — Concerning the Hilbert sixteenth problem
    • Yu. Ilyashenko and S. Yakovenko — Finite cyclicity of elementary polycycles in generic families
    • S. Trifonov — Desingularization in families of analytic differential equations
    • O. Kleban — Order of the topologically sufficient jet of a smooth vector field on the real plane at a singular point of finite multiplicity
    • A. Kotova and V. Stanzo — On few-parameter generic families of vector fields on the two-dimensional sphere
    • S. Yakovenko — A geometric proof of the Bautin theorem
  • 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
Advances in the Mathematical Sciences
Volume: 1651995; 219 pp
MSC: Primary 34

This book examines qualitative properties of vector fields in the plane, in the spirit of Hilbert's Sixteenth Problem. Two principal topics explored are bifurcations of limit cycles of planar vector fields and desingularization of singular points for individual vector fields and for analytic families of such fields. In addition to presenting important new developments in this area, this book contains an introductory paper which outlines the general context and describes connections between the papers in the volume. The book will appeal to researchers and graduate students working in the qualitative theory of ordinary differential equations and dynamical systems.

Readership

Researchers and graduate students working in the qualitative theory of ordinary differential equations.

  • Chapters
  • Yu. Ilyashenko and S. Yakovenko — Concerning the Hilbert sixteenth problem
  • Yu. Ilyashenko and S. Yakovenko — Finite cyclicity of elementary polycycles in generic families
  • S. Trifonov — Desingularization in families of analytic differential equations
  • O. Kleban — Order of the topologically sufficient jet of a smooth vector field on the real plane at a singular point of finite multiplicity
  • A. Kotova and V. Stanzo — On few-parameter generic families of vector fields on the two-dimensional sphere
  • S. Yakovenko — A geometric proof of the Bautin theorem
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
Please select which format for which you are requesting permissions.