On the 1:4 resonance problem: analysis of the bifurcation set

The central question is: what happens near a bifurcation where a closed orbit of a vector field looses its stability in a 1:4 resonance? This leads to the study of a classical codimension-two bifurcation, a Hopf bifurcation of a planar
diffeomorphism with 1:4 resonance. The diffeomorphism can be approximated up to flat terms by a Z4-equivariant planar vector field composed with the rotation by π/2.

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Summary

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