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Singularity theory and equivariant bifurcation problems with parameter symmetry

  • Jacques-Élie Furter (a1), Angela Maria Sitta (a2) and Ian Stewart (a3)

The study of equivariant bifurcation problems via singularity theory (Golubitsky and Schaeffer[8], Golubitsky, Stewart and Schaeffer[9]) has been mainly concerned with models exhibiting spontaneous symmetry-breaking. The solutions of such bifurcation problems lose symmetry as the parameters vary, but the equations that they satisfy retain the same symmetry throughout.

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[1] T. J. Bridges and J. E. Furter . Singularity theory and equivariant symplectic maps. Lecture Notes in Math. 1558 (Springer-Verlag, 1993).

[5] T. Gaffney . Some new results in the classification theory of bifurcation problems. In Multiparameter bifurcation theory. Contemporary Mathematics 56 (Amer. Math. Soc., 1986).

[6] M. Golubitsky and M. Roberts . A classification of degenerate Hopf bifurcations withO(2) symmetry. J. Diff. Eg. 69 (1987), 216264.

[7] M. Golubitsky and D. G. Schaeffer . A theory for imperfect bifurcation theory via singularity theory. Commun. Pure Appl. Math. 32 (1979), 2198.

[8] M. Golubitsky and D. G. Schaeffer . Singularities and groups in bifurcation theory, vol. I, Applied Math. Sci. 51 (Springer-Verlag, 1985).

[9] M. Golubitsky , I. Stewart and D. G. Schaeffer . Singularities and groups in bifurcation theory, vol. II, Applied Math. Sci. 69 (Springer-Verlag, 1988).

[13] G. Schwartz . Smooth functions invariant under the action of a compact Lie group. Topology 14 (1975), 6368.

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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