$SO(3)\times S^1$-equivariant degree with applications to symmetric bifurcation problems: the case of one free parameter

Zolman Balanov, Wiesław Krawcewicz, Heinrich Steinlein

DOI: http://dx.doi.org/10.12775/TMNA.2002.040

Abstract


The reduced equivariant degree for $G=SO(3)\times S^1$ is introduced and
studied in the case of one free parameter equivariant maps. Computational
and multiplication tables for the reduced $SO(3)\times S^1$-equivariant
degree are presented together with an application to an $SO(3)$-symmetric
Hopf bifurcation problem. A method for classification of $SO(3)$-symmetric
bifurcations is established.

Keywords


equivariant degree; symmetric Hopf bifurcation; steady-state bifurcation

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