Bifurcation without Parameters

Nonfiction, Science & Nature, Mathematics, Differential Equations, Mathematical Analysis
Cover of the book Bifurcation without Parameters by Stefan Liebscher, Springer International Publishing
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Author: Stefan Liebscher ISBN: 9783319107776
Publisher: Springer International Publishing Publication: November 8, 2014
Imprint: Springer Language: English
Author: Stefan Liebscher
ISBN: 9783319107776
Publisher: Springer International Publishing
Publication: November 8, 2014
Imprint: Springer
Language: English

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.

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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.

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