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Resonant Homoclinic Bifurcations with Orbit Flips and Inclination Flips

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DOI: 10.4236/am.2013.42042    3,284 Downloads   5,485 Views  
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Homoclinic bifurcation with one orbit flip, two inclination flips and resonance in the tangent directions of homoclinic orbit is considered. By studying the associated successor functions constructed from a local active coordinate system, we prove the existence of double 1-periodic orbit, 1-homoclinic orbit, and also some coexistence conditions of 1-periodic orbit and 1-homoclinic orbit.

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The authors declare no conflicts of interest.

Cite this paper

T. Zhang, "Resonant Homoclinic Bifurcations with Orbit Flips and Inclination Flips," Applied Mathematics, Vol. 4 No. 2, 2013, pp. 279-284. doi: 10.4236/am.2013.42042.


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