TITLE:
Resonant Homoclinic Bifurcations with Orbit Flips and Inclination Flips
AUTHORS:
Tiansi Zhang
KEYWORDS:
Orbit Flip; Inclination Flip; Resonance
JOURNAL NAME:
Applied Mathematics,
Vol.4 No.2,
February
22,
2013
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.