| Description |
1 online resource |
| Contents |
List of Tables; Notation and Conventions; 1 Polynomial Ideals and Their Varieties; 1.1 Fundamental Concepts; 1.2 The Ideal Membership Problem and Gröbner Bases; 1.3 Basic Properties and Algorithms; 1.4 Decomposition of Varieties; 1.5 Notes and Complements; Exercises; 2 Stability and Normal Forms; 2.1 Lyapunov's Second Method; 2.2 Real Normal Forms; 2.3 Analytic and Formal Normal Forms; 2.4 Notes and Complements; Exercises; 3 The Center Problem; 3.1 The Poincaré First Return Map and the Lyapunov Numbers; 3.2 Complexification of Real Systems, Normal Forms, and the CenterProblem |
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3.3 The Center Variety3.4 Focus Quantities and Their Properties; 3.5 Hamiltonian and Reversible Systems; 3.6 Darboux Integrals and Integrating Factors; 3.7 Applications: Quadratic Systems and a Family of Cubic Systems; 3.8 The Center Problem for Liénard Systems; 3.9 Notes and Complements; Exercises; 4 The Isochronicity and Linearizability Problems; 4.1 The Period Function; 4.2 Isochronicity Through Normal Forms and Linearizability; 4.3 The Linearizability Quantities; 4.4 Darboux Linearization; 4.5 Linearizable Quadratic Centers; 4.6 Notes and Complements; Exercises |
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5 Invariants of the Rotation Group5.1 Properties of Invariants; 5.2 The Symmetry Ideal and the Set of Time-Reversible Systems; 5.3 Axes of Symmetry of a Plane System; 5.4 Notes and Complements; Exercises; 6 Bifurcations of Limit Cycles and Critical Periods; 6.1 Bautin's Method for Bifurcation Problems; 6.2 The Cyclicity Problem; 6.3 The Cyclicity of Quadratic Systems and a Family of Cubic Systems; 6.4 Bifurcations of Critical Periods; 6.5 Notes and Complements; Exercises; Appendix; References; Index of Notation; Index |
| Summary |
Using a computational algebra approach, this text addresses the center and cyclicity problems as behaviors of dynamical systems and families of polynomial systems. It covers the main properties of ideals in polynomial rings and their affine varieties followed by a discussion on the theory of normal forms and stability of differential equations |
| Analysis |
wiskunde |
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mathematics |
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veeltermen |
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polynomials |
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algebra |
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partial differential equations |
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differentiaalvergelijkingen |
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differential equations |
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computerwiskunde |
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computational mathematics |
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numerieke wiskunde |
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numerical mathematics |
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Mathematics (General) |
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Wiskunde (algemeen) |
| Bibliography |
Includes bibliographical references (pages 313-321) and index |
| Notes |
English |
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Print version record |
| Subject |
Polynomials.
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Polynomials
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| Form |
Electronic book
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| Author |
Shafer, Douglas S.
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| ISBN |
9780817647278 |
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0817647279 |
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9780817647261 |
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0817647260 |
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