Codimension-4 resonant homoclinic bifurcations with orbit flips and inclination flips |
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Authors: | Tian Si Zhang De Ming Zhu |
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Affiliation: | 1. College of Science, University of Shanghai for Science and Technology, Shanghai 200093, P. R. China;2. Department of Mathematics, East China Normal University, Shanghai 200062, P. R. China |
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Abstract: | The paper studies a codimension-4 resonant homoclinic bifurcation with one orbit flip and two inclination flips, where the resonance takes place in the tangent direction of homoclinic orbit. Local active coordinate system is introduced to construct the Poincaré returning map, and also the associated successor functions. We prove the existence of the saddle-node bifurcation, the perioddoubling bifurcation and the homoclinic-doubling bifurcation, and also locate the corresponding 1-periodic orbit, 1-homoclinic orbit, double periodic orbits and some 2n-homoclinic orbits. |
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Keywords: | Orbit flip inclination flip resonant homoclinic-doubling bifurcations |
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