Hardcover ISBN:  9780821803622 
Product Code:  TRANS2/165 
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Electronic ISBN:  9781470433765 
Product Code:  TRANS2/165.E 
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Book DetailsAmerican Mathematical Society Translations  Series 2Advances in the Mathematical SciencesVolume: 165; 1995; 219 ppMSC: 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.
ReadershipResearchers and graduate students working in the qualitative theory of ordinary differential equations.

Table of Contents

Cover

Title page

Copyright page

Contents

Concerning the Hilbert sixteenth problem

Finite cyclicity of elementary polycycles in generic families

Desingularization in families of analytic differential equations

Order of the topologically sufficient jet of a smooth vector field on the real plane at a singular point of finite multiplicity

On fewparameter generic families of vector fields on the twodimensional sphere

A geometric proof of the Bautin theorem

Back Cover


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

Cover

Title page

Copyright page

Contents

Concerning the Hilbert sixteenth problem

Finite cyclicity of elementary polycycles in generic families

Desingularization in families of analytic differential equations

Order of the topologically sufficient jet of a smooth vector field on the real plane at a singular point of finite multiplicity

On fewparameter generic families of vector fields on the twodimensional sphere

A geometric proof of the Bautin theorem

Back Cover