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A theory for imperfect bifurcation via singularity theory
Author(s) -
Golubitsky M.,
Schaeffer D.
Publication year - 1979
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.3160320103
Subject(s) - imperfect , singularity , singularity theory , citation , mathematics , mathematical economics , calculus (dental) , discrete mathematics , computer science , library science , philosophy , mathematical analysis , linguistics , medicine , dentistry
: This paper applies the theory of singularities of differentiable mappings - specifically the unfolding theorem - to study the effect of imperfections in a system subject to bifurcation. In a number of special cases we have classified (up to a suitable equivalence) all the possible perturbations of the bifurcation equations by a finite number of imperfection parameters. These cases include both bifurcation from a double eigenvalue and from a simple eigenvalue degenerate in the sense of Crandall-Rabinowitz.