A codimension-4 homoclinic bifurcation with one orbit flip and one inclination flip at principal eigenvalue direction resonance is considered. By introducing a local active coordinate system in some small neighborhood of homoclinic orbit, we get the Poincaré return map and the bifurcation equation. A detailed investigation produces the number and the existence of 1-homoclinic orbit, 1-periodic orbit, and double 1-periodic orbits. We also locate their bifurcation surfaces in certain regions.
"Resonant Homoclinic Flips Bifurcation in Principal Eigendirections." Abstr. Appl. Anal. 2013 1 - 7, 2013. https://doi.org/10.1155/2013/267826