Abstract
The Liapunov-Schmidt reduction procedure is used to study the existence of periodic orbits in a parametrized family of autonomous differential equations near a 1:2 resonant equilibrium point. This corresponds to a Hopf-Hopf mode interaction where the imaginary eigenvalues are in 1 to 2 ratio. We assume the existence of a distinguished bifurcation parameter, and then use singularity theory in order to classify the generic perfect and perturbed (unfolded) bifurcation diagrams for periodic orbits.
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© 1994 Springer Science+Business Media Dordrecht
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Leblanc, V.G., Langford, W.F. (1994). Bifurcation of Periodic Orbits in 1:2 Resonance: A Singularity Theory Approach. In: Chossat, P. (eds) Dynamics, Bifurcation and Symmetry. NATO ASI Series, vol 437. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0956-7_18
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DOI: https://doi.org/10.1007/978-94-011-0956-7_18
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