Bifurcation without Parameters

• Main Author: Liebscher, Stefan (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2015.
• Series: Lecture Notes in Mathematics, 2117
• Subjects: Mathematics.; Dynamics.; Ergodic theory.; Differential equations.; Partial differential equations.; Ordinary Differential Equations.; Partial Differential Equations.; Dynamical Systems and Ergodic Theory.
• Physical Description: XII, 142 p. 34 illus., 29 illus. in color. online resource.
• ISBN: 9783319107776
• ISSN: 0075-8434 ;

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.