Qualitative theory of planar differential systems
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....
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| Formatua: | Livre numérique |
| Hizkuntza: | Anglais |
| Argitaratua: |
Berlin, Heidelberg :
Springer Berlin Heidelberg
2006.
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| Edizioa: | 1st ed. 2006. |
| Saila: | Universitext
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| Gaiak: | |
| Sarrera elektronikoa: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Oharra: |
L'impression du document génère 314 p. Description d'après consultation du 20 avril 2011 Titre provenant de la page de titre du document numérisé Numérisation de l'édition de Berlin : Springer, cop. 2006 Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Qualitative Theory of Planar Differential Systems, Texte imprimé, 9783540821595 • Qualitative Theory of Planar Differential Systems, Texte imprimé, 9783540328933 |
| Gaia: | 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 |
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| Alearen deskribapena: | L'impression du document génère 314 p. Description d'après consultation du 20 avril 2011 Titre provenant de la page de titre du document numérisé Numérisation de l'édition de Berlin : Springer, cop. 2006 Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Formatua: | Nécessite un lecteur de fichier PDF |
| Bibliografia: | Bibliogr. p. [285]-293. Index |
| ISBN: | 9783540329022 |
| ISSN: | 2191-6675 |
| Sartu: | Accès en ligne pour les établissements français bénéficiaires des licences nationales Accès soumis à abonnement pour tout autre établissement Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. chttps://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 |