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- W2123229729 abstract "Resonance tongues and their boundaries are studied for nondegenerate and (certain) degenerate Hopf bifurcations of maps using singularity theory methods of equivariant contact equivalence and universal unfoldings. We recover the standard theory of tongues (the nondegenerate case) in a straightforward way and we find certain surprises in the tongue boundary structure when degeneracies are present. For example, the tongue boundaries at degenerate singularities in weak resonance are much blunter than expected from the nondegenerate theory. Also at a semi-global level we find `pockets' or `flames' that can be understood in terms of the swallowtail catastrophe." @default.
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- W2123229729 date "2003-06-06" @default.
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- W2123229729 title "The geometry of resonance tongues: a singularity theory approach" @default.
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- W2123229729 doi "https://doi.org/10.1088/0951-7715/16/4/319" @default.
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