Resonant Homoclinic Bifurcations with Orbit Flips and Inclination Flips

DOI: 10.4236/am.2013.42042   PDF   HTML   XML   3,392 Downloads   5,508 Views  

Abstract

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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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.

Conflicts of Interest

The authors declare no conflicts of interest.

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