《极限环分支理论(精)》编著者Han Maoan。
This book introduces the bifurcation theory of limit cycles of planar systems withmultiple parameters. It is focused on the most recent developments in this field andprovides major advances in fundamental theory of limit cycles. The main topics includeHopf bifurcation of limit cycles from a center or a focus, homoclinic bifurcations near ahomoclinic or a heteroclinic loop,and the number of limit cycles in global bifurcations ofnear-Hamiltonian polynomial systems of arbitrary degree. This book will be of use tograduate mathematics students as well as scientists.
Han Maoan is a professor at the Institute of Mathematical Sciences of Shanghai NormalUniversity. He has been working on the research of differential equations and dynamicalsystems for 30 years with 300 papers published.
Preface
Chapter 1 Limit Cycle and Its Perturbations
1.1 Basic notations and facts
1.2 Further discussion on property of limit cycles
1.3 Perturbations of a limit cycle
Chapter 2 Focus Values and Hopf Bifurcation
2.1 Poincare map and focus value
2.2 Normal form and Poincare-Lyapunov technique
2.3 Hopf bifurcation near a focus and systems with symmetry
2.4 Degenerate Hopf bifurcation near a center
2.5 Hopf bifurcation for Lienard systems
2.6 Hopf bifurcation for some polynomial systems
Chapter 3 Perturbations of Hamiltonian Systems
3.1 General theory
3.2 Limit cycles near homoclinic and heteroclinic loops
3.3 Finding more limit cycles by Melnikov functions
3.4 Limit cycle bifurcations near a nilpotent center
3.5 Limit cycle bifurcations with a nilpotent cusp
3.6 Limit cycle bifurcations with a nilpotent saddle
Chapter 4 Stability of Homoclinic Loops and Limit Cycle Bifurcations
4.1 Local behavior near a saddle
4.2 Stability of a homoclinic loop and bifurcation near it
4.3 Homoclinic and heteroclinic bifurcations in near-Hamiltonian systems
Chapter 5 The Number of Limit Cycles of Polynomial Systems
5.1 Introduction
5.2 Some fundamental results
5.3 Further study for general polynomial systems
Bibliography
Index
