**American Mathematical Society Translations - Series 2
Advances in the Mathematical Sciences**

1995; 219 pp; Hardcover

MSC: Primary 34;

Print ISBN: 978-0-8218-0362-2

Product Code: TRANS2/165

Print ISBN: 978-0-8218-0362-2

Product Code: TRANS2/165

List Price: $122.00

Individual Member Price: $97.60

**Electronic ISBN: 978-1-4704-3376-5
Product Code: TRANS2/165.E**

List Price: $122.00

Individual Member Price: $97.60

# Concerning the Hilbert 16th Problem

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*Yu. Ilyashenko; S. Yakovenko*

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

## Concerning the Hilbert 16th Problem

- Cover Cover11
- Title page v6
- Copyright page vi7
- Contents vii8
- Concerning the Hilbert sixteenth problem 110
- Finite cyclicity of elementary polycycles in generic families 2130
- Desingularization in families of analytic differential equations 97106
- Order of the topologically sufficient jet of a smooth vector field on the real plane at a singular point of finite multiplicity 131140
- On few-parameter generic families of vector fields on the two-dimensional sphere 155164
- A geometric proof of the Bautin theorem 203212
- Back Cover Back Cover1231