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Bücher Englische Bücher Wissen & Bildung Naturwissenschaft, Medizin, Informatik, Technik Mathematik Arithmetik & Algebra The Hopf Bifurcation and Its Applications
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The Hopf Bifurcation and Its Applications
J. E. Marsden, M. McCracken (Taschenbuch, Englisch)
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Beschreibung
The goal of these notes is to give a reasonahly com plete, although not exhaustive, discussion of what is commonly referred to as the Hopf bifurcation with applications to spe cific problems, including stability calculations. Historical ly, the subject had its origins in the works of Poincare [1] around 1892 and was extensively discussed by Andronov and Witt [1] and their co-workers starting… around 1930. Hopf's basic paper [1] appeared in 1942. Although the term "Poincare Andronov-Hopf bifurcation" is more accurate (sometimes Friedrichs is also included), the name "Hopf Bifurcation" seems more common, so we have used it. Hopf's crucial contribution was the extension from two dimensions to higher dimensions. The principal technique employed in the body of the text is that of invariant manifolds. The method of Ruelle Takens [1] is followed, with details, examples and proofs added. Several parts of the exposition in the main text come from papers of P. Chernoff, J. Dorroh, O. Lanford and F. Weissler to whom we are grateful. The general method of invariant manifolds is common in dynamical systems and in ordinary differential equations: see for example, Hale [1,2] and Hartman [1]. Of course, other methods are also available. In an attempt to keep the picture balanced, we have included samples of alternative approaches. Specifically, we have included a translation (by L. Howard and N. Kopell) of Hopf's original (and generally unavailable) paper. 106,99 €
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Technische Daten
Erscheinungsdatum
17.08.1976
Sprache
Englisch
EAN
9780387902005
Herausgeber
Springer US
Serien- oder Bandtitel
Applied Mathematical Sciences
Sonderedition
Nein
Autor
J. E. Marsden, M. McCracken
Seitenanzahl
408
Einbandart
Taschenbuch
Schlagwörter
Bifurcation, Calculation, Invariant, Manifold, Morphism, dynamical systems, equation, proof, theorem, matrix theory
Thema-Inhalt
PBF - Algebra
Höhe
235 mm
Breite
15.5 cm
Transparenz & Sicherheit
Hersteller: Humana, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com, Springer Nature Customer Service Center GmbH
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