Descripción del título
Qualitative Theory of Plana...
The book deals essentially 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: based on both algebraic manipulation and numerical calculation, this was conceived for the purpose of drawing "Polynomial Planar Phase Portraits" on part of the plane, or on a Poincaré compactification, or even on a Poincaré-Lyapunov compactification of the plane. 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. The book is very appropriate for a first course in dynamical systems, presenting the basic notions in the study of individual two dimensional systems. Not only does it provide simple and appropriate proofs, but it also contains a lot of exercises and presents a survey of interesting results with the necessary references to the literature
Monografía
monografia Rebiun03603507 https://catalogo.rebiun.org/rebiun/record/Rebiun03603507 cr nn 008mamaa 100301s2006 gw | s |||| 0|eng d 9783540329022 978-3-540-32902-2 10.1007/978-3-540-32902-2 doi UR0288973 UPNA0210561 UPVA 996884339903706 UAM 991007838425804211 CUNEF 991000429336008131 CBUC 991008391059706706 NoBUC-cargaSpringer. SpMaUCSC PBKJ bicssc MAT007000 bisacsh Dumortier, Freddy. author Qualitative Theory of Planar Differential Systems Recurso electrónico] by Freddy Dumortier, Jaume Llibre, Joan C. Artés XVI, 302 p. 123 illus. online resource XVI, 302 p. 123 illus. Basic Results on the Qualitative Theory of Differential Equations -- Normal Forms and Elementary Singularities -- Desingularization of Nonelementary Singularities -- Centers and Lyapunov Constants -- Poincaré and PoincaréLyapunov 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 Acceso restringido a usuarios UCM = Restricted use for UCM patrons The book deals essentially 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: based on both algebraic manipulation and numerical calculation, this was conceived for the purpose of drawing "Polynomial Planar Phase Portraits" on part of the plane, or on a Poincaré compactification, or even on a Poincaré-Lyapunov compactification of the plane. 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. The book is very appropriate for a first course in dynamical systems, presenting the basic notions in the study of individual two dimensional systems. Not only does it provide simple and appropriate proofs, but it also contains a lot of exercises and presents a survey of interesting results with the necessary references to the literature Llibre, Jaume author Artés, Joan C. author Springer Books