Información General

• Autores: Freddy Dumortier , Joan Carles Artés Ferragud , Jaume Llibre
• Editores: Berlin : Springer, cop. 2006
• Año de publicación: 2006
• País: Alemania
• Idioma: inglés
• ISBN: 3-540-32893-9, 978-3-540-32893-3, 978-3-540-32902-2
• Texto completo no disponible (Saber más ...)

Resumen

• 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.

Otros catálogos

• Red de Bibliotecas Universitarias (REBIUN)

Índice

• Basic Results on the Qualitative Theory of Differential Equations.- Normal Forms and Elementary Singularities.- Desingularization of Non-elementary Singularities. Centers and Lyapunov Constants. - Poincaré and Poincaré-Lyapunov Compactification.- Indices of Planar Singular Points.- Limit Cycles and Structural Stability.- Integrability and Algebaric Solutions in Polynomial Vector Fields.- Polynomial Planar Phase Portraits.- Examples for Running P4. - Bibliography.