The Center and Cyclicity Problems: A Computational Algebra Approach

Machine derived contents note: Polynomial Ideals and Their Varieties Fundamental Concepts The Ideal Membership Problem and Gr6bner Bases Basic Properties and Algorithms Decomposition of Varieties Notes and Complements Exercises 51 Stability and Normal Forms 57 Lyapunov's Second Method 57 Real Normal Forms 62 Analytic and Formal Normal Forms 68 Notes and Complements 83 Exercises 84 The Center Problem 89 The Poincard First Return Map and the Lyapunov Numbers 91 Complex iication of Real Systems, Normal Forms, and the Center Problem The Center Variety Focus Quantities and Their Properties Hamiltonian and Reversible Systems Darboux Integrals and Integrating Factors Applications: Quadratic Systems and a Family of Cubic Systems The Center Problem for Lienard Systems Notes and Complements he Isochronicity and Linearizability Problems The Period Function Isochronicity Through Normal Forms and Linearizahility The Linearizability Quantities Darboux Linearization Linearizable Quadratic Centers Notes and Complements Invariants of the Rotation Group Properties of Invariants The Symmetry Ideal and the Set of Time-Reversible Systems Axes of Symmetry of a Plane System Notes and Complements Bifurcations of Limit Cycles and Critical Periods Bautin's Method for Bifurcation Problems The Cyclicity Problem The Cyclicity of Quadratic Systems and a Family of Cubic Systems Bifurcations of Critical Periods Notes and Complements