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 Poincarémap and focus value

2.2 Normal form and Poincaré-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 Liénard 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