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  • 1
    Electronic Resource
    Electronic Resource
    Spontaneous symmetry breaking in higher dimensional fixed point spaces (1992)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 43 (1992), S. 430-448 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Summary We investigate the branching of solutions of equivariant problems where the equivariant branching lemma does not apply, because the relevant subgroup ∑ has a 2 dimensional fixed point space. First we look at a case where ∑ is a maximal isotropy subgroup, then we consider the case where it is a submaximal isotropy subgroup.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00946239
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    Paper (German National Licenses)
    Fulltext
  • 2
    Electronic Resource
    Electronic Resource
    Bifurcation analysis for spherically symmetric systems using invariant theory (1997)
    Springer
    Journal of dynamics and differential equations 9 (1997), S. 535-560 
    Details
    ISSN: 1572-9222
    Keywords: Bifurcation analysis ; spherically symmetric systems ; invariant theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We study a degenerate steady state bifurcation problem with spherical symmetry. This singularity, with the five dimensional irreducible action ofO(3), has been studied by several authors for codimensions up to 2. We look at the case where the topological codimension is 3, theC ∞-codimension is 5. We find a tertiary Hopf bifurcation and a heteroclinic orbit. Our analysis does not use any specific properties of the five dimensional representation and can in principle be used for higher representations as well. The computations are based on invariant theory and orbit space reduction.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02219397
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Steady-State bifurcation with 0(3)-Symmetry (1991)
    Springer
    Archive for rational mechanics and analysis 113 (1991), S. 313-376 
    Details
    ISSN: 1432-0673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00374697
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    Paper (German National Licenses)
    Fulltext
  • 4
    Electronic Resource
    Electronic Resource
    Symmetry-breaking at non-positive solutions of semilinear elliptic equations (1994)
    Springer
    Archive for rational mechanics and analysis 126 (1994), S. 299-331 
    Details
    ISSN: 1432-0673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We consider symmetry-breaking bifurcations at non-positive, radially symmetric solutions of semilinear elliptic equations on a ball with Dirichlet boundary conditions. For nonlinearities which are asymptotically affine linear, we find solutions at which the symmetry breaks. The kernel of the linearized equation at these solutions is an absolutely irreducible representation of the group O(n). For this kind of equation a transversality condition is satisfied if the perturbation of the affine linear problem is small enough. Thus we obtain, by the equivariant branching lemma, a large variety of isotropy subgroups of O(n) which occur as symmetries of the bifurcating solution branches.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00380895
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    Paper (German National Licenses)
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  • 5
    Book
    Book
    Methods in equivariant bifurcations and dynamical systems; 15 (2000)
    Singapore u.a. :World Scientific,
    Details
    Title: Methods in equivariant bifurcations and dynamical systems; 15
    Author: Chossat, Pascal
    Contributer: Lauterbach, Reiner
    Publisher: Singapore u.a. :World Scientific,
    Year of publication: 2000
    Pages: 404 S.
    Series Statement: Advanced series in nonlinear dynamics 15
    Type of Medium: Book
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    ZIB Catalog
    Zuse Institute Berlin get availability status
  • 6
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    Unknown
    Automatic classification of normal forms (1995)
    Details
    Publication Date: 2014-02-26
    Description: The aim of this paper is to demonstrate a specific application of Computer Algebra to bifurcation theory with symmetry. The classification of different bifurcation phenomena in case of several parameters is automated, based on a classification of Gröbner bases of possible tangent spaces. The computations are performed in new coordinates of fundamental invariants and fundamental equivariants, with the induced weighted ordering. In order to justify the approach the theory of intrinsic modules is applied. Results for the groups $D_3, Z_2,$ and $ Z_2\times Z_2$ demonstrate that the algorithm works independent of the group and that new results are obtained.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
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