Qualitative theory of planar differential systems
著者
書誌事項
Qualitative theory of planar differential systems
（Universitext）
Springer, c2006
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注記
"With 123 figures and 10 tables"
Includes bibliographical references (p. [285]-293) and index
内容説明・目次
内容説明
This book deals with systems of polynomial autonomous ordinary differential equations in two real variables. The emphasis is mainly qualitative, although attention is also given to more algebraic aspects as a thorough study of the center/focus problem and recent results on integrability. In the last two chapters the performant software tool P4 is introduced. From the start, differential systems are represented by vector fields enabling, in full strength, a dynamical systems approach. All essential notions, including invariant manifolds, normal forms, desingularization of singularities, index theory and limit cycles, are introduced and the main results are proved for smooth systems with the necessary specifications for analytic and polynomial systems.
目次
Basic Results on the Qualitative Theory of Differential Equations.- Normal Forms and Elementary Singularities.- Desingularization of Nonelementary Singularities.- Centers and Lyapunov Constants.- Poincare and Poincare-Lyapunov Compactification.- Indices of Planar Singular Points.- Limit Cycles and Structural Stability.- Integrability and Algebraic Solutions in Polynomial Vector Fields.- Polynomial Planar Phase Portraits.- Examples for Running P4.
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