The classification of reversible-equivariant steady-state bifurcations on self-dual spaces

• Autores: P. H. Baptistelli, M. Manoel
• Localización: Mathematical proceedings of the Cambridge Philosophical Society, ISSN 0305-0041, Vol. 145, Nº 2, 2008, págs. 379-401
• Idioma: inglés
• DOI: 10.1017/s0305004108001400
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• Resumen

  • In this paper we apply singularity theory methods to the classification of reversible-equivariant steady-state bifurcations depending on one real parameter. We assume that the group of symmetries and reversing symmetries is a compact Lie group G, and the equivalence is defined in order to preserve these symmetries and reversing symmetries in the normal forms and their unfoldings. When the representation of G is self-dual, we show that the classification can be reduced to the standard equivariant context. In this case, we establish a one-to-one association between the classification of bifurcations in the reversible-equivariant context and the classification of purely equivariant bifurcations related to them. As an application of the results, we obtain the classification of self-dual representations of Z2 Z2 and D4 on the plane.