Planar Dynamical Systems: Selected Classical Problems

Yirong Liu; Jibin Li; Wentao Huang

Open Access Published by De Gruyter 2014

Planar Dynamical Systems

Selected Classical Problems

Yirong Liu , Jibin Li and Wentao Huang
Together with: Science Press

https://doi.org/10.1515/9783110298369

Overview
Contents

About this book

In 2008, November 23-28, the workshop of ”Classical Problems on Planar Polynomial Vector Fields ” was held in the Banff International Research Station, Canada. Called "classical problems", it was concerned with the following:

(1) Problems on integrability of planar polynomial vector fields.

(2) The problem of the center stated by Poincaré for real polynomial differential systems, which asks us to recognize when a planar vector field defined by polynomials of degree at most n possesses a singularity which is a center.

(3) Global geometry of specific classes of planar polynomial vector fields.

(4) Hilbert’s 16th problem.

These problems had been posed more than 110 years ago. Therefore, they are called "classical problems" in the studies of the theory of dynamical systems. The qualitative theory and stability theory of differential equations, created by Poincaré and Lyapunov at the end of the 19th century, had major developments as two branches of the theory of dynamical systems during the 20th century. As a part of the basic theory of nonlinear science, it is one of the very active areas in the new millennium.

This book presents in an elementary way the recent significant developments in the qualitative theory of planar dynamical systems. The subjects are covered as follows: the studies of center and isochronous center problems, multiple Hopf bifurcations and local and global bifurcations of the equivariant planar vector fields which concern with Hilbert’s 16th problem.

The book is intended for graduate students, post-doctors and researchers in dynamical systems. For all engineers who are interested in the theory of dynamical systems, it is also a reasonable reference. It requires a minimum background of a one-year course on nonlinear differential equations.

Author / Editor information

Yirong Liu, Jibin Li and Wentao Huang, Zhejiang Normal University, Jinhua, Zhejiang, P. R. China.

Supplementary Materials

Contents

Topics

Frontmatter Open Access Download PDF	V
Preface Open Access Download PDF	IX
Contents Open Access Download PDF	XIX
Chapter 1. Basic Concept and Linearized Problem of Systems Open Access Download PDF	1
Chapter 2. Focal Values, Saddle Values and Singular Point Values Open Access Download PDF	69
Chapter 3. Multiple Hopf Bifurcations Open Access Download PDF	97
Chapter 4. Isochronous Center In Complex Domain Open Access Download PDF	111
Chapter 5. Theory of Center-Focus and Bifurcation of Limit Cycles at Infinity of a Class of Systems Open Access Download PDF	138
Chapter 6. Theory of Center-Focus and Bifurcations of Limit Cycles for a Class of Multiple Singular Points Open Access Download PDF	180
Chapter 7 On Quasi Analytic Systems Open Access Download PDF	205
Chapter 8. Local and Non-Local Bifurcations of Perturbed Zq-Equivariant Hamiltonian Vector Fields Open Access Download PDF	232
Chapter 9. Center-Focus Problem and Bifurcations of Limit Cycles for a Z2-Equivariant Cubic System Open Access Download PDF	272
Chapter 10. Center-Focus Problem and Bifurcations of Limit Cycles for Three-Multiple Nilpotent Singular Points Open Access Download PDF	308
Bibliography Open Access Download PDF	342
Index Open Access Download PDF	369

(Deutsch)

Language: English
Publisher: De Gruyter
Audience: Graduate students, post-doctors and researchers in Mathematics, engeneers, academic libraries.
Pages
- Front matter: 18
- Main content: 371
Keywords: Center and isochronous center; Multiple Hopf and global bifurcations; Limit cycle; Planar dynamical system; Hilbert's 16th problem

eBook

Published: October 29, 2014
ISBN: 9783110298369

Hardcover

Published: September 29, 2014
ISBN: 9783110298291