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.
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Lauterbach, R., Sanders, J.A. Bifurcation analysis for spherically symmetric systems using invariant theory. J Dyn Diff Equat 9, 535–560 (1997). https://doi.org/10.1007/BF02219397
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DOI: https://doi.org/10.1007/BF02219397