In two earlier papers, the motion of a structure induced by vortex shedding was investigated for the cases of resonance and order three subharmonic resonance. In both cases classes of unbounded solutions exist and the size and boundary of the domain of stability dividing these from bounded solutions is therefore of great interest. In this paper we show that, for light damping, the domain of stability has an extremely complex boundary due to the presence of heteroclinic orbits. In addition, it may be considerably smaller than might be expected. The method employed is quite general and the conclusions appear significant for a number of other problems in nonlinear oscillations.

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