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Synergetics pp 34-38 | Cite as

Bifurcation of a Continuum of Unstable Modes

  • K. Kirchgässner
Conference paper
Part of the Springer Series in Synergetics book series (SSSYN, volume 2)

Abstract

In this contribution we consider model equations of increasing complexity which exhibit bifurcation in a continuum of points. In spite of the wealth of solutions present there is - under certain simple geometrical conditions - a selection principle yielding only a finite number of stable solutions. The geometrical conditions mentioned guarantee essentially “supercritical” bifurcation for the continuum as an entity and thus reflect at this level the now classical result for simple eigenvalue bifurcation [2], [7].

Keywords

Periodic Solution Singular Solution Small Solution Simple Eigenvalue Nonzero Solution 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1977

Authors and Affiliations

  • K. Kirchgässner

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