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  • 1
    Electronic Resource
    Electronic Resource
    Hopf Bifurcation in the presence of symmetry (1985)
    Springer
    Archive for rational mechanics and analysis 87 (1985), S. 107-165 
    Details
    ISSN: 1432-0673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Using group theoretic techniques, we obtain a generalization of the Hopf Bifurcation Theorem to differential equations with symmetry, analogous to a static bifurcation theorem of Cicogna. We discuss the stability of the bifurcating branches, and show how group theory can often simplify stability calculations. The general theory is illustrated by three detailed examples: O(2) acting on R 2, O(n) on R n , and O(3) in any irreducible representation on spherical harmonics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00280698
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