Chapter 1 Focal Values, Saddle Values and Singular Point Values 1.1 Successor Functions and Properties of Focal Values 1.2 Poincare Formal Series and Algebraic Equivalence 1.3 Singular Point Values and Conditions of Integrability 1.4 Linear Recursive Formulas for the Computation of Singular Point Values 1.5 The Algebraic Construction of Singular Values 1.6 Elementary Invariants of the Cubic Systems 1.7 Singular Point Values of the Quadratic Systems and the Homogeneous Cubic Systems Chapter 2 Theory of Center-focus for a Class of Infinite Singular Points and Higher-order Singular Points 2.1 Conversion of the Questions 2.2 Theory of Center-focus at the Infinity for a Class of Systems 2.3 Theory of Center-focus of Higher-order Singular Points for a Class of Systems 2.4 The Construction of Singular Point Values of Higher-order Singular Points and Infinity 2.5 Translational Invariance of the Singular Values at Infinity Chapter 3 Multiple Hopf Bifurcations 3.1 The Zeros of Successor Functions in the Polar Coordinates 3.2 Analytic Equivalence 3.3 Weak Bifurcation Function Some Polynomial Vector Fields 4.1 Cubic Systems Created Four Limit Cycles at Infinity 4.2 Cubic Systems Created Seven Limit Cycles at Infinity Chapter 5 Local and Non-local Bifurcations of Perturbed Zq-equivatiant Hamiltonian Vector Fields 5.1 Zq-equivariant Planar Vector Fields and an Example 5.2 The Method of Detection Functions: Rough Perturbations of Zp- equivariant Hamiltonian Vector Fields 5.3 Bifurcations of Limit Cycles of a Z2- equivariant Perturbed Hamiltonian Vector Fields 5.4 The Rate of Growth of Hilbert Number H(n) with n Chapter 6 Isochronous Center 6.1 Isochronous Centers and Period Constants 6.2 Complex Period Constants 6.3 Application of the Method of Section 6.2 6.4 The Method of Time-angle Difference 6.5 Conditions of Isochronous Center for a Cubic System 6.6 Isochronous Centers at Infinity of Polynomial Systems Chapter 7 On Quasi Analytic Systems 7.1 Preliminary 7.2 Reduction of the Problems 7.3 Focal Values, Periodic Constants and First Integrals of (7.2.3) 7.4 Singular Point Values and Bifurcations of Limit Cycles of Quasi-quadratic Systems 7.5 Integrability of Quasi-quadratic Systems 7.6 Node Point Values 7.7 Isochronous Center of Quasi-quadratic Systems Chapter 8 Complete Study on a Bi-center Problem for the Z2-equivariant Cubic Vector Fields 8.1 Introduction and Main Results 8.2 The Reduction of System Having Two Elementary Focuses at (1,0) and (-1,0) 8.3 Lyapunov Constants. Invariant Integrals and the Necessary and Sufficient Conditions of the Existence for the Bi-center 8.4 The Conditions of Six-order Fine Focus of (8.3.2) and Bifurcations of Limit Cycles Bibliography
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