The Cusp Horseshoe and its Bifurcations in the Unfolding of an Inclination-flip Homoclinic Orbit
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Resonant homoclinic ip bifurcations
This paper studies three-parameter unfoldings of resonant orbit ip and inclination ip homoclinic orbits. First all known results on codimension-two unfoldings of homoclinic ip bifurcations are presented. Then we show that the orbit ip and inclination ip both feature the creation and destruction of a cusp horseshoe. Furthermore, we show near which resonant ip bifurcations a homoclinic-doubling c...
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Homoclinic bifurcations are important phenomena that cause global re-arrangements of the dynamics in phase space, including changes to basins of attractions and the generation of chaotic dynamics. We consider here a homoclinic (or connecting) orbit that converges in both forward and backward time to a saddle equilibrium of a three-dimensional vector field. We assume that the saddle is such that...
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تاریخ انتشار 2005