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Bifurcation without Parameters
Taschenbuch von Stefan Liebscher
Sprache: Englisch

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Beschreibung
Targeted at mathematicians having at least a basic familiarity with classical bifurcation theory, this monograph provides a systematic classification and analysis of bifurcations without parameters in dynamical systems. Although the methods and concepts are briefly introduced, a prior knowledge of center-manifold reductions and normal-form calculations will help the reader to appreciate the presentation. Bifurcations without parameters occur along manifolds of equilibria, at points where normal hyperbolicity of the manifold is violated. The general theory, illustrated by many applications, aims at a geometric understanding of the local dynamics near the bifurcation points.
Targeted at mathematicians having at least a basic familiarity with classical bifurcation theory, this monograph provides a systematic classification and analysis of bifurcations without parameters in dynamical systems. Although the methods and concepts are briefly introduced, a prior knowledge of center-manifold reductions and normal-form calculations will help the reader to appreciate the presentation. Bifurcations without parameters occur along manifolds of equilibria, at points where normal hyperbolicity of the manifold is violated. The general theory, illustrated by many applications, aims at a geometric understanding of the local dynamics near the bifurcation points.
Zusammenfassung

This is the first systematic treatment of the topic

Numerous figures augment the analytic treatment and assist in understanding

The abstract theory is complemented by many applications

Inhaltsverzeichnis

Introduction.- Methods & Concepts.- Cosymmetries.- Codimension One.- Transcritical Bifurcation.- Poincar¿e-Andronov-Hopf Bifurcation.- Application: Decoupling in Networks.- Application: Oscillatory Profiles.- Codimension Two.- egenerate Transcritical Bifurcation.- egenerate Andronov-Hopf Bifurcation.- Bogdanov-Takens Bifurcation.- Zero-Hopf Bifurcation.- Double-Hopf Bifurcation.- Application: Cosmological Models.- Application: Planar Fluid Flow.- Beyond Codimension Two.- Codimension-One Manifolds of Equilibria.- Summary & Outlook.

Details
Erscheinungsjahr: 2014
Fachbereich: Analysis
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 156
Reihe: Lecture Notes in Mathematics
Inhalt: xii
142 S.
5 s/w Illustr.
29 farbige Illustr.
142 p. 34 illus.
29 illus. in color.
ISBN-13: 9783319107769
ISBN-10: 3319107763
Sprache: Englisch
Herstellernummer: 86374125
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Liebscher, Stefan
Auflage: 2015
Hersteller: Springer International Publishing
Lecture Notes in Mathematics
Maße: 235 x 155 x 9 mm
Von/Mit: Stefan Liebscher
Erscheinungsdatum: 19.11.2014
Gewicht: 0,248 kg
preigu-id: 105178174
Zusammenfassung

This is the first systematic treatment of the topic

Numerous figures augment the analytic treatment and assist in understanding

The abstract theory is complemented by many applications

Inhaltsverzeichnis

Introduction.- Methods & Concepts.- Cosymmetries.- Codimension One.- Transcritical Bifurcation.- Poincar¿e-Andronov-Hopf Bifurcation.- Application: Decoupling in Networks.- Application: Oscillatory Profiles.- Codimension Two.- egenerate Transcritical Bifurcation.- egenerate Andronov-Hopf Bifurcation.- Bogdanov-Takens Bifurcation.- Zero-Hopf Bifurcation.- Double-Hopf Bifurcation.- Application: Cosmological Models.- Application: Planar Fluid Flow.- Beyond Codimension Two.- Codimension-One Manifolds of Equilibria.- Summary & Outlook.

Details
Erscheinungsjahr: 2014
Fachbereich: Analysis
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 156
Reihe: Lecture Notes in Mathematics
Inhalt: xii
142 S.
5 s/w Illustr.
29 farbige Illustr.
142 p. 34 illus.
29 illus. in color.
ISBN-13: 9783319107769
ISBN-10: 3319107763
Sprache: Englisch
Herstellernummer: 86374125
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Liebscher, Stefan
Auflage: 2015
Hersteller: Springer International Publishing
Lecture Notes in Mathematics
Maße: 235 x 155 x 9 mm
Von/Mit: Stefan Liebscher
Erscheinungsdatum: 19.11.2014
Gewicht: 0,248 kg
preigu-id: 105178174
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