Resonant Homoclinic Bifurcations with Orbit Flips and Inclination Flips

Tiansi Zhang

College of Science, University of Shanghai for Science and Technology, Shanghai, China.

DOI: 10.4236/am.2013.42042                

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.

Keywords

Orbit Flip; Inclination Flip; Resonance

Conflicts of Interest

The authors declare no conflicts of interest.

References

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